Daily Papers

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for post-training large language models. While Group Relative Policy Optimization (GRPO) is widely adopted, its coarse credit assignment uniformly penalizes failed rollouts, lacking the token-level focus needed to efficiently address specific deviations. Self-Distillation Policy Optimization (SDPO) addresses this by providing denser, more targeted logit-level supervision that facilitates rapid early improvement, yet it frequently collapses during prolonged training. We trace this late-stage instability to two intrinsic flaws: self-distillation on already-correct samples introduces optimization ambiguity, and the self-teacher's signal reliability progressively degrades. To resolve these issues, we propose Sample-Routed Policy Optimization (SRPO), a unified on-policy framework that routes correct samples to GRPO's reward-aligned reinforcement and failed samples to SDPO's targeted logit-level correction. SRPO further incorporates an entropy-aware dynamic weighting mechanism to suppress high-entropy, unreliable distillation targets while emphasizing confident ones. Evaluated across five benchmarks and two model scales, SRPO achieves both the rapid early improvement of SDPO and the long-horizon stability of GRPO. It consistently surpasses the peak performance of both baselines, raising the five-benchmark average on Qwen3-8B by 3.4% over GRPO and 6.3% over SDPO, while simultaneously yielding moderate response lengths and lowering per-step compute cost by up to 17.2%.

Large language models trained with reinforcement learning (RL) for mathematical reasoning face a fundamental challenge: on problems the model cannot solve at all - "cliff" prompts - the RL gradient vanishes entirely, preventing any learning signal from reaching these failure modes. We introduce Hybrid Distillation Policy Optimization (HDPO), which augments standard RL with privileged self-distillation targeting cliff prompts. On each training step, HDPO identifies prompts where all rollouts fail, generates privileged rollouts by providing the model with ground-truth information, filters for correct solutions, and distills the teacher's token-level distribution into the student. Because teacher and student share the same weights - differing only in their input - the realizability gap is provably bounded, unlike cross-model distillation. We prove that R=1 filtered privileged generation recovers the optimal KL-regularized RL policy in the hard-threshold limit. Experiments on OpenMathInstruct-2 with Qwen2.5-Math-1.5B-Instruct show that HDPO consistently improves coverage metrics (pass@4 by +0.8-1.1%, pass@8 by +0.4-1.7%) while maintaining greedy accuracy, with the distillation weight lambda providing direct control over the exploration-exploitation tradeoff.

Continual post-training enables foundation models to acquire new knowledge while preserving existing capabilities. Recent work suggests that on-policy learning can mitigate forgetting, with on-policy self-distillation emerging as a particularly attractive approach. In this work, we revisit this optimistic view through self-distillation policy optimization (SDPO). Our experiments show that SDPO can accelerate in-domain specialization when teacher signals are stable and well aligned, but it struggles to generalize to out-of-distribution scenarios. In continual post-training, SDPO exhibits stronger forgetting and can even collapse, whereas on-policy reinforcement learning methods such as GRPO adapt more conservatively and better preserve prior capabilities. Further analyses reveal that denser self-distillation induces larger drift in both parameter space and response space, and can amplify high-frequency formatting artifacts through a self-reinforcing teacher--student loop. These findings suggest that on-policy data alone is insufficient for continual learning. Dense self-distillation can accelerate specialization when teacher targets are stable and token-level supervision is reliable, but it should not be treated as a default stabilizer for continual post-training. Our code is available at https://github.com/Moenupa/SDPO-CL.

Large language models are increasingly post-trained with reinforcement learning in verifiable domains such as code and math. Yet, current methods for reinforcement learning with verifiable rewards (RLVR) learn only from a scalar outcome reward per attempt, creating a severe credit-assignment bottleneck. Many verifiable environments actually provide rich textual feedback, such as runtime errors or judge evaluations, that explain why an attempt failed. We formalize this setting as reinforcement learning with rich feedback and introduce Self-Distillation Policy Optimization (SDPO), which converts tokenized feedback into a dense learning signal without any external teacher or explicit reward model. SDPO treats the current model conditioned on feedback as a self-teacher and distills its feedback-informed next-token predictions back into the policy. In this way, SDPO leverages the model's ability to retrospectively identify its own mistakes in-context. Across scientific reasoning, tool use, and competitive programming on LiveCodeBench v6, SDPO improves sample efficiency and final accuracy over strong RLVR baselines. Notably, SDPO also outperforms baselines in standard RLVR environments that only return scalar feedback by using successful rollouts as implicit feedback for failed attempts. Finally, applying SDPO to individual questions at test time accelerates discovery on difficult binary-reward tasks, achieving the same discovery probability as best-of-k sampling or multi-turn conversations with 3x fewer attempts.

Large language models (LLMs) have achieved remarkable progress in mathematical reasoning, but this ability is not equally accessible across languages. Especially low-resource languages exhibit much lower reasoning performance. To address this, we propose Crosslingual On-Policy Self-Distillation (COPSD), which transfers a model's own high-resource reasoning behavior to low-resource languages. COPSD uses the same model as student and teacher: the student sees only the low-resource problem, while the teacher receives privileged crosslingual context, including the problem translation and reference solution in English. Training minimizes full-distribution token-level divergence on the student's own rollouts, providing dense supervision while avoiding the sparsity and instability of outcome-only reinforcement learning (RL). Experiments on 17 low-resource African languages show that COPSD consistently improves low-resource mathematical reasoning across model sizes and substantially outperforms Group Relative Policy Optimization (GRPO). Further analyses show that COPSD improves answer-format adherence, strengthens test-time scaling, and generalizes to harder multilingual reasoning benchmarks, with especially large gains for lower-resource languages. We make our code and data available at: https://github.com/cisnlp/COPSD.

Outcome-based reinforcement learning provides a stable optimization backbone for language agents, but its sparse trajectory-level rewards provide little guidance on which intermediate decisions should be reinforced or suppressed. On-policy self-distillation offers dense token-level supervision, yet existing skill-conditioned variants often rely on external skill memories or retrieved privileged context, which are costly to maintain and can be mismatched with the state distribution induced by the current policy in multi-turn interaction. We propose OPID (On-Policy Skill Distillation), a framework that extracts skill supervision directly from completed on-policy trajectories. OPID represents trajectory hindsight as hierarchical skills: episode-level skills capture global workflows or failure-avoidance rules, while step-level skills capture local decision knowledge at critical timesteps. A critical-first routing mechanism uses step-level skills when critical decisions are identified and falls back to episode-level skills as default guidance otherwise. The selected skill is injected into the interaction history, allowing the old policy to re-score the same sampled response under both original and skill-augmented contexts. The resulting log-probability shift yields a token-level self-distillation advantage, which is combined with the outcome advantage for policy optimization. OPID thus preserves RL as the primary training objective while introducing dense, distribution-matched hindsight supervision. Experiments on ALFWorld, WebShop and Search-based QA demonstrate that OPID generally improves agent performance, sample efficiency, and robustness over outcome-only RL and existing skill-distillation baselines. Our code is available at https://github.com/jinyangwu/OPID/tree/main.

When a model produces a correct solution under reinforcement learning with verifiable rewards (RLVR), every token receives the same reward signal regardless of whether it was a decisive reasoning step or a grammatical filler. A natural fix is to condition the model on the correct answer as a teacher, identifying tokens it would have generated differently had it known the answer. Prior work shows this either corrupts training by leaking the answer into the gradient, or produces a weak signal that cannot distinguish decisive steps from filler, since both look equally surprising relative to the model's baseline. We propose Contrastive Evidence Policy Optimization (CEPO), which asks a sharper question at every token: not just "does the correct answer favor this token?" but "does the correct answer favor it while the wrong answer disfavors it?" A token satisfying both is a genuine reasoning step; one satisfying neither is filler. The wrong-answer teacher is constructed from rejected rollouts already in the training batch, incurring no additional sampling cost. We prove CEPO inherits all structural safety guarantees of the prior state of the art while strictly sharpening credit at decisive tokens, with the improvement vanishing exactly at filler positions. Empirically, CEPO achieves 43.43% and 60.56% average accuracy across five multimodal mathematical reasoning benchmarks at 2B and 4B scale, respectively, versus 41.17% and 57.43% for GRPO under identical training budgets. Distribution-matching self-distillation methods (OPSD, SDPO) fall below the untrained baseline, empirically confirming the information leakage our theory predicts. Our code is available at https://github.com/ahmedheakl/CEPO.

Self-distillation improves reasoning in large language models by using the model's own rollouts as training signal, typically through implicit logit-level alignment that minimizes KL divergence toward a privileged target distribution. However, because this supervision is generated via uncontrolled sampling, it provides no diagnostic insight into the model's specific errors or corrective guidance for its individual failure patterns. Consequently, the model learns to imitate a privileged distribution rather than receiving fine-grained corrections that pinpoint where and why its reasoning fails. In this paper, we propose Trajectory-Augmented Policy Optimization (TAPO), which advances self-distillation from implicit distributional alignment to explicit trajectory construction. During RL training, the model produces both correct and incorrect rollouts to the same query, and TAPO leverages this contrastive structure to construct micro-reflective corrections, new training trajectories that retain the model's erroneous reasoning up to the point of failure, then insert a natural-language diagnosis and corrected reasoning guided by a correct reference from the same sampling group. Since each trajectory is anchored in the learner's own prefix and solutions, the corrective signal preserves the model's on-policy distribution to a greater extent than the position-wise alignment imposed by KL-based methods. To integrate these trajectories, TAPO introduces difficulty-aware candidate selection at the model's capability boundary and decoupled advantage estimation to prevent gradient contamination. Experiments on AIME 2024, AIME 2025, and HMMT 2025 show that TAPO achieves consistent improvements over GRPO under the same number of training steps. Further analysis demonstrates that TAPO strengthens both first-pass reasoning and error-correction effectiveness.

Enabling large language models to achieve stable self-improvement without external expert supervision remains a central challenge in complex reasoning tasks. Existing self-distillation and reinforcement learning methods lack explicit mechanisms for tracking problem-level learning progress and adapting optimization strategies accordingly. Consequently, training may over-optimize easy problems, receive weak supervision from hard problems, and fail to sufficiently explore borderline cases. To resolve these issues, we propose DRIFT, an online self-evolution policy optimization framework for large language models. DRIFT regulates the model's self-improvement process through the joint use of Difficulty Routing and Rhythm Gating. The former identifies the model's learning state at the problem level and dynamically allocates self-distillation and reinforcement learning signals, while the latter refines policy updates at the token level, concentrating exploration on critical reasoning positions. By further incorporating a success buffer and a two-stage curriculum learning strategy, DRIFT preserves high-quality historical experience while progressively guiding the model from reliable behavior acquisition toward stable policy evolution. Evaluated across five benchmarks and three model scales, DRIFT surpasses the peak performance of both GRPO and SDPO across all evaluated metrics. On the average score over the five benchmarks, DRIFT achieves 79.5%, outperforming GRPO by 9.5% and SDPO by 7.5%, establishing a new state-of-the-art result. Notably, on ToolUse, DRIFT reaches an accuracy of 79.2%, improving over GRPO by 13.5% and SDPO by 10.7%, setting a new state-of-the-art and substantially outperforming all concurrent methods.

Real-time video generation via diffusion is essential for building general-purpose multimodal interactive AI systems. However, the simultaneous denoising of all video frames with bidirectional attention via an iterative process in diffusion models prevents real-time interaction. While existing distillation methods can make the model autoregressive and reduce sampling steps to mitigate this, they focus primarily on text-to-video generation, leaving the human-AI interaction unnatural and less efficient. This paper targets real-time interactive video diffusion conditioned on a multimodal context, including text, image, and audio, to bridge the gap. Given the observation that the leading on-policy distillation approach Self Forcing encounters challenges (visual artifacts like flickering, black frames, and quality degradation) with multimodal conditioning, we investigate an improved distillation recipe with emphasis on the quality of condition inputs as well as the initialization and schedule for the on-policy optimization. On benchmarks for multimodal-conditioned (audio, image, and text) avatar video generation including HDTF, AVSpeech, and CelebV-HQ, our distilled model matches the visual quality of the full-step, bidirectional baselines of similar or larger size with 20x less inference cost and latency. Further, we integrate our model with audio language models and long-form video inference technique Anchor-Heavy Identity Sinks to build LiveTalk, a real-time multimodal interactive avatar system. System-level evaluation on our curated multi-turn interaction benchmark shows LiveTalk outperforms state-of-the-art models (Sora2, Veo3) in multi-turn video coherence and content quality, while reducing response latency from 1 to 2 minutes to real-time generation, enabling seamless human-AI multimodal interaction.

Long-horizon agentic tasks pose a fundamental credit assignment challenge for outcome-base reinforcement learning: trajectory-level rewards verify final correctness but provide limited guidance on which intermediate reasoning steps or tool interactions contribute to the outcome. The difficulty is especially pronounced in multi-turn search agents, where successful trajectories may contain misleading actions and failed trajectories may contain valuable evidence-gathering steps. We propose PBSD (Privileged Bayesian Self-Distillation), a Bayes-calibrated self-distillation method for fine-grained credit assignment under sparse final rewards. PBSD measures trajectory quality through the posterior-to-prior probability ratio of the verified answer and applies Bayes' rule to convert this hard-to-estimate answer-side ratio into a tractable likelihood ratio between a standard student model and a privileged answer-conditioned teacher model. Autoregressive decomposition of this Bayesian evidence score yields turn-level signals that identify whether each intermediate turn supports or undermines the verified outcome. Consequently, PBSD provides a principled and elegant reweighting scheme that transforms sparse outcome supervision into Bayes-calibrated turn-level credit signals, while remaining fully compatible with standard policy optimization. Experiments demonstrate that PBSD consistently enhances performance across both in-domain and out-of-domain settings, and effectively transfers knowledge from short-context training to long-context inference, suggesting that its fine-grained credit assignment mechanism facilitates more effective policy learning and yields improved generalization.

While safety alignment for Multimodal Large Language Models (MLLMs) has gained significant attention, current paradigms primarily target malicious intent or situational violations. We propose shifting the safety frontier toward consequence-driven safety, a paradigm essential for the robust deployment of autonomous and embodied agents. To formalize this shift, we introduce OOD-MMSafe, a benchmark comprising 455 curated query-image pairs designed to evaluate a model's ability to identify latent hazards within context-dependent causal chains. Our analysis reveals a pervasive causal blindness among frontier models, with the highest 67.5% failure rate in high-capacity closed-source models, and identifies a preference ceiling where static alignment yields format-centric failures rather than improved safety reasoning as model capacity grows. To address these bottlenecks, we develop the Consequence-Aware Safety Policy Optimization (CASPO) framework, which integrates the model's intrinsic reasoning as a dynamic reference for token-level self-distillation rewards. Experimental results demonstrate that CASPO significantly enhances consequence projection, reducing the failure ratio of risk identification to 7.3% for Qwen2.5-VL-7B and 5.7% for Qwen3-VL-4B while maintaining overall effectiveness.

On-policy distillation (OPD) and on-policy self-distillation (OPSD) have emerged as promising post-training methods for large language models, offering dense token-level supervision on trajectories sampled from the model's own policy. However, existing results on their effectiveness remain mixed: while OP(S)D has shown promise in system prompt and knowledge internalization, recent studies also report instability and degradation. In this work, we present a comprehensive empirical study of when OPD and OPSD work, when they fail, and why. We find that OPD on mathematical reasoning is highly sensitive to teacher choice and loss formulation, whereas OPSD fails in our tested settings due to test-time absence of instance-specific privileged information (PI). In contrast, OPSD is effective when PI represents a shared latent rule, such as a system prompt or alignment preference. We identify three failure mechanisms: (1) distribution mismatch between teacher and student caused by conditioning on student-generated prefixes, (2) optimization instability from biased TopK reverse-KL gradients, and (3) an OPSD-specific limitation where the student learns a PI-free policy that aggregates PI-conditioned teachers, which is insufficient when PI is instance-specific. We further show that stop-gradient TopK objectives, RLVR-adapted teachers, and SFT-stabilized students mitigate these failures.

Extending the effective context length of large language models (LLMs) remains a central challenge for real-world applications. While recent post-training methods have made progress in long-context scaling, they either rely on high-quality supervision data or sparse sequence-level rewards, leading to unstable and inefficient optimization. We propose OPSDL, an On-Policy Self-Distillation method for enhancing the Long-context capabilities of LLMs. Unlike other recent self-distillation methods that inject privileged information and rely on the model's in-context learning ability to act as a teacher, OPSDL leverages the model's own inherently strong short-context capability as a self-teacher to supervise its own generation in long-context scenarios. The model first generates responses conditioned on the full long-context, then the self-teacher provides per-token supervision signals via point-wise reverse KL divergence under the relevant extracted short-context. This dense token-level signal encourages faithful use of relevant evidence and mitigates hallucinations induced by irrelevant context. We evaluate OPSDL on long-context benchmarks across a range of models from 7B to 32B parameters. Results show consistent and substantial improvements across varying context lengths, outperforming standard post-training approaches such as SFT and DPO with higher sample efficiency. Notably, these gains are achieved without degrading general short-context performance. These findings highlight the effectiveness of OPSDL as a scalable and stable approach for long-context learning.

On-policy self-distillation (OPSD) has proven effective for post-training large language models (LLMs), yet its application to diffusion LLMs (dLLMs) remains unexplored. Existing OPSD methods are inherently autoregressive-centric. They inject privileged information via left-to-right prefix conditioning with token-level divergence supervision, a design that fundamentally conflicts with the arbitraryorder generation of dLLMs. We introduce d-OPSD, the first OPSD framework tailored for dLLMs. Our approach makes two core contributions. First, we reframe self-teacher construction by using self-generated answers as suffix conditioning, enabling the student model to learn from "self future-experience" rather than privileged prefixes. Second, we shift supervision from token-level to step-level, aligning training with the iterative denoising process of dLLMs. Experiments across four reasoning benchmarks show that d-OPSD consistently outperforms RLVR and SFT baselines with superior sample efficiency, requiring only around 10% of the optimization steps by RLVR and opening a promising pathway for dLLM posttraining. The code is available at https://github.com/xingzhejun/d-OPSD.

Graphical User Interface (GUI) grounding maps natural language instructions to the visual coordinates of target elements and serves as a core capability for autonomous GUI agents. Recent reinforcement learning methods (e.g., GRPO) have achieved strong performance, but they rely on expensive multiple rollouts and suffer from sparse signals on hard samples. These limitations make on-policy self-distillation (OPSD), which provides dense token-level supervision from a single rollout, a promising alternative. However, its applicability to GUI grounding remains unexplored. In this paper, we present GUI-SD, the first OPSD framework tailored for GUI grounding. First, it constructs a visually enriched privileged context for the teacher using a target bounding box and a Gaussian soft mask, providing informative guidance without leaking exact coordinates. Second, it employs entropy-guided distillation, which adaptively weights tokens based on digit significance and teacher confidence, concentrating optimization on the most impactful and reliable positions. Extensive experiments on six representative GUI grounding benchmarks show that GUI-SD consistently outperforms GRPO-based methods and naive OPSD in both accuracy and training efficiency. Code and training data are available at https://zhangyan-ucas.github.io/GUI-SD/.

Due to constraints on privacy, cost, and latency, on-premise deployment of small models is increasingly common. However, most practical pipelines stop at supervised fine-tuning (SFT) and fail to reach the reinforcement learning (RL) alignment stage. The main reason is that RL alignment typically requires either expensive human preference annotation or heavy reliance on high-quality reward models with large-scale API usage and ongoing engineering maintenance, both of which are ill-suited to on-premise settings. To bridge this gap, we propose a positive-unlabeled (PU) RL distillation method for on-premise small-model deployment. Without human-labeled preferences or a reward model, our method distills the teacher's preference-optimization capability from black-box generations into a locally trainable student. For each prompt, we query the teacher once to obtain an anchor response, locally sample multiple student candidates, and perform anchor-conditioned self-ranking to induce pairwise or listwise preferences, enabling a fully local training loop via direct preference optimization or group relative policy optimization. Theoretical analysis justifies that the induced preference signal by our method is order-consistent and concentrates on near-optimal candidates, supporting its stability for preference optimization. Experiments demonstrate that our method achieves consistently strong performance under a low-cost setting.

Large language models are increasingly trained as interactive agents for long-horizon tasks involving multi-turn interaction, tool use, and environment feedback. Outcome-based reinforcement learning (RL) provides a practical optimization paradigm, but its sparse trajectory-level rewards offer limited guidance on intermediate decisions, leaving a supervision gap between episode-level outcomes and token-level policy learning. We propose SEED (SElf-Evolving On-Policy Distillation), a self-evolving framework that converts completed on-policy trajectories into training-time hindsight skills and distills their behavioral effect back into the policy model. SEED first fine-tunes the policy to analyze completed trajectories and generate natural-language skills that capture reusable workflows, decisive observations, or failure-avoidance rules. During RL, the current policy both collects trajectories and serves as the analyzer that extracts hindsight skills from them. Policy updates therefore improve subsequent decision making and skill analysis together, allowing hindsight supervision to evolve with the policy. SEED then re-scores the sampled actions under ordinary and skill-augmented contexts, converting the skill-induced probability shift into a dense token-level on-policy distillation signal. This signal is jointly optimized with outcome-based RL, keeping the auxiliary supervision aligned with the current trajectory distribution. Extensive experiments on text-based and vision-based agentic tasks show that SEED consistently improves performance and sample efficiency, exhibiting robust generalization to unseen scenarios. Our code is available at https://github.com/jinyangwu/SEED.

As an increasing majority of global video content is consumed on social platforms for interactive social purposes, video generation models built for social worlds are important but largely overlooked by previous studies. In this work, we define the position of social world models and build a prototype model as the first step towards this goal. While previous world models successfully simulate physical environments or gaming world exploration, they remain fundamentally detached from human-centric social dynamics. To bridge this gap as the first step to social world models, we present MaineCoon, the first real-time audio-visual autoregressive model that has 22B parameters and is capable of real-time streaming generation and sub-second interaction, with a record-breaking frame rate of up to 47.5 FPS, on a single GPU. To the best of our knowledge, MaineCoon is also the first real-time audio-visual generation model specifically optimized for social-interactive applications. To enable efficient and stable training, we introduce several novel techniques into MaineCoon, including self-resampling, cross-modal representation alignment, domain-aware preference optimization, and reinforced online-policy distillation (ROPD). We also design the first agentic streaming inference framework that supports thousand-second-scale or even longer generation while mitigating drift with agentic cache management and prompt planing. These innovations significantly accelerate training while optimizing real-time inference performance. We believe this work not only sets a new state-of-the-art (SOTA) performance benchmark for high-quality, low-latency, and long-horizon audio-visual autoregressive models, but also points out the paradigm shift desired for next-generation AI-native social platforms.

On-policy distillation (OPD) has become a popular training paradigm in the LLM community. This paradigm selects a larger model as the teacher to provide dense, fine-grained signals for each sampled trajectory, in contrast to reinforcement learning with verifiable rewards (RLVR), which only obtains sparse signals from verifiable outcomes in the environment. Recently, the community has explored on-policy self-distillation (OPSD), where the same model serves as both teacher and student, with the teacher receiving additional privileged information such as reference answers to enable self-evolution. This paper demonstrates that learning signals solely derived from the privileged teacher result in severe information leakage and unstable long-term training. Accordingly, we identify the optimal niche for self-distillation and propose RLSD (RLVR with Self-Distillation). Specifically, we leverage self-distillation to obtain token-level policy differences for determining fine-grained update magnitudes, while continuing to use RLVR to derive reliable update directions from environmental feedback (e.g., response correctness). This enables RLSD to simultaneously harness the strengths of both RLVR and OPSD, achieving a higher convergence ceiling and superior training stability.

On-policy self-distillation, where a language model conditions on privileged context to supervise its own generations, is a promising source of dense supervision for sparse-reward reinforcement learning. Actually, it can be instantiated as an auxiliary full-vocabulary student-to-teacher reverse Kullback-Leibler divergence loss. We therefore propose SDPG, a self-distilled policy-gradient framework that combines group-relative verifier advantages with normalized standard deviation, exact full-vocabulary on-policy self-distillation, as well as reference-policy KL regularization. Empirically, SDPG improves stability and performance over RLVR and self-distillation baselines. The code is available at https://github.com/lauyikfung/SDPG.

Reinforcement learning (RL) has been widely used to train LLM agents for multi-turn interactive tasks, but its sample efficiency is severely limited by sparse rewards and long horizons. On-policy self-distillation (OPSD) alleviates this by providing dense token-level supervision from a privileged teacher that has access to ground-truth answers. However, such fixed privileged information cannot capture the diverse valid strategies in agent tasks, and naively combining OPSD with RL often leads to training collapse. To address these limitations, we introduce Skill-SD, a framework that turns the agent's own trajectories into dynamic training-only supervision. Completed trajectories are summarized into compact natural language skills that describe successful behaviors, mistakes, and workflows. These skills serve as dynamic privileged information conditioning only the teacher, while the student always acts under the plain task prompt and learns to internalize the guidance through distillation. To stabilize the training, we derive an importance-weighted reverse-KL loss to provide gradient-correct token-level distillation, and dynamically synchronize the teacher with the improving student. Experimental results on agentic benchmarks demonstrate that Skill-SD substantially outperforms the standard RL baseline, improving both vanilla GRPO (+14.0%/+10.9% on AppWorld/Sokoban) and vanilla OPD (+42.1%/+40.6%). Project page: https://k1xe.github.io/skill-sd/

On-policy self-distillation (OPSD) is an emerging LLM post-training paradigm in which the model serves as its own teacher: conditioned on privileged information such as a reference trace or hint, the same policy provides dense token-level supervision on its own rollouts. However, recent studies show that OPSD degrades complex reasoning by suppressing predictive uncertainty, which supports exploration and hypothesis revision. Our token-level analysis shows that this failure arises from applying a uniform direction of teacher supervision across tokens with different uncertainty levels: conformity to the privileged self-teacher suppresses exploration at high entropy, while deviation from the teacher degrades step accuracy at low entropy. Accordingly, we propose Direction-Adaptive Self-Distillation (DASD), which reframes privileged self-distillation from uniform teacher imitation into entropy-routed directional supervision: high-entropy tokens are pushed away from the privileged teacher to preserve exploration, while low-entropy tokens are pulled toward the teacher to stabilize step-level execution. Across six mathematical reasoning benchmarks, DASD achieves the best macro Avg@16 over strong RLVR and self-distillation baselines. Pass@k, reasoning-health, and generalization analyses show that these average gains come from preserving exploration without sacrificing step-level execution.

Diffusion large language models (dLLMs) generate text by iteratively denoising a masked sequence, offering a parallel alternative to autoregressive models, but eliciting strong reasoning through post-training remains difficult: supervised fine-tuning is off-policy and suffers from exposure bias, while reinforcement learning gives only sparse, sequence-level rewards and is hard to apply without tractable sequence likelihoods. On-policy self-distillation (OPSD) offers a promising alternative, using one model as both student and teacher to provide dense, token-level, on-policy supervision, but its effectiveness hinges on giving the teacher privileged information (PI) - typically an instance-specific ground-truth reference unavailable at inference - so the student ends up distilling a weak PI-free consensus policy that yields little improvement on dLLM reasoning. We introduce dOPSD, which instead derives the teacher's privilege directly from the student's own denoising trajectory, evaluating masked positions using later, more-decoded steps of that same trajectory rather than an external label, so the teacher's advantage emerges from the model's own decoding process; on Dream and LLaDA, dOPSD improves both in-domain math reasoning and out-of-domain code generation, outperforming supervised and on-policy baselines.

Reinforcement learning (RL) has emerged as a central paradigm for post-training LLM agents, yet its trajectory-level reward signal provides only coarse supervision for long-horizon interaction. On-Policy Self-Distillation (OPSD) complements RL by introducing dense token-level guidance from a teacher branch augmented with privileged context. However, transferring OPSD to multi-turn agents proves problematic: compounding multi-turn instability destabilizes supervision, while skill-conditioned privileged guidance requires asymmetric treatment for negative teacher rejections may arise from imperfect skills retrieval or utilization. We introduce SDAR (Self-Distilled Agentic Reinforcement Learning), which treats OPSD as a gated auxiliary objective while keeping RL as the primary optimization backbone. SDAR maps detached token-level signals into a sigmoid gate, strengthening distillation on teacher-endorsed positive-gap tokens and softly attenuating negative teacher rejections. Across the Qwen2.5 and Qwen3 families on ALFWorld, WebShop, and Search-QA, SDAR substantially improves over GRPO (+9.4% on ALFWorld, +7.0% on Search-QA, +10.2% on WebShop-Acc), avoids the instability of naive GRPO+OPSD, and consistently outperforms hybrid RL--OPSD baselines across model scales.

Knowledge distillation has become a primary mechanism for transferring reasoning and domain expertise from frontier Large Language Models (LLMs) to smaller, deployable students. However, the dominant paradigm remains off-policy: students train on static teacher-generated data and never encounter their own errors during learning. This train--test mismatch, an instance of exposure bias, causes prediction errors to compound autoregressively at inference time. On-Policy Distillation (OPD) addresses this by letting the student generate its own trajectories and receive teacher feedback on these self-generated outputs, grounding distillation in the theory of interactive imitation learning. Despite rapid growth spanning divergence minimization, reward-guided learning, and self-play, the OPD literature remains fragmented with no unified treatment. This survey provides the first comprehensive overview of OPD for LLMs. We introduce a unified f-divergence framework over on-policy samples and organize the landscape along three orthogonal dimensions: feedback signal (logit-based, outcome-based, or self-play), teacher access (white-box, black-box, or teacher-free), and loss granularity (token-level, sequence-level, or hybrid). We systematically analyze representative methods, examine industrial deployments, and identify open problems including distillation scaling laws, uncertainty-aware feedback, and agent-level distillation.

Training-time privileged information (PI) can enable language models to succeed on tasks they would otherwise fail, making it a powerful tool for reinforcement learning in hard, long-horizon settings. However, transferring capabilities learned with PI to policies that must act without it at inference time remains a fundamental challenge. We study this problem in the context of distilling frontier models for multi-turn agentic environments, where closed-source systems typically hide their internal reasoning and expose only action trajectories. This breaks standard distillation pipelines, since successful behavior is observable but the reasoning process is not. For this, we introduce π-Distill, a joint teacher-student objective that trains a PI-conditioned teacher and an unconditioned student simultaneously using the same model. Additionally, we also introduce On-Policy Self-Distillation (OPSD), an alternative approach that trains using Reinforcement Learning (RL) with a reverse KL-penalty between the student and the PI-conditioned teacher. We show that both of these algorithms effectively distill frontier agents using action-only PI. Specifically we find that π-Distill and in some cases OPSD, outperform industry standard practices (Supervised finetuning followed by RL) that assume access to full Chain-of-Thought supervision across multiple agentic benchmarks, models, and forms of PI. We complement our results with extensive analysis that characterizes the factors enabling effective learning with PI, focusing primarily on π-Distill and characterizing when OPSD is competitive.

We study multi-domain LLM training in which two models, each stronger in a different domain, co-evolve by tutoring each other through on-policy feedback. Unlike one-way distillation or single-model fine-tuning, our goal is mutual Pareto improvement: each model improves across domains without losing its original strength. To this end, we propose On-Policy Co-Distillation (OPCoD), where each student's self-distillation is conditioned on its own correct rollout and feedback from its peer. To make feedback exchange effective, OPCoD uses cognizance-based gating to decide when to give feedback and feedback anchoring to ground feedback in the problem. On Science Q\&A tasks, OPCoD consistently outperforms baselines and achieves Pareto improvement across all evaluated domain pairs and students.

Reinforcement learning from verifiable rewards (RLVR) suffers from sparse outcome signals, creating severe exploration bottlenecks on complex reasoning tasks. Recent on-policy self-distillation methods attempt to address this by utilizing language feedback to generate dense, token-level supervision. However, these approaches rely on a fixed, passive teacher to interpret the feedback. As the student policy improves, the teacher's zero-shot assessment capabilities plateau, ultimately halting further learning. To overcome this, we propose Variational Policy Distillation (VPD), a framework that formalizes learning from language feedback as a Variational Expectation-Maximization (EM) problem. VPD co-evolves both policies: in the E-step, the teacher is actively refined on trajectory outcomes via an adaptive trust-region update, translating textual feedback into a dynamically improved target token distribution. In the M-step, the student internalizes this dense distributional guidance on its own on-policy rollouts. By continuously improving the teacher's ability to extract actionable signals from textual critique, VPD overcomes the limitations of passive distillation. Evaluated across diverse sources of diagnostic feedback on scientific reasoning and code generation tasks, VPD consistently outperforms both standard RLVR and existing self-distillation baselines. Finally, by stress-testing our framework on rigid mathematical reasoning and cold-start regimes, we illuminate the fundamental bounds of feedback-driven self-distillation compared to pure environment-driven RL.

On-policy distillation (OPD) trains a student on its own trajectories with token-level teacher feedback and often outperforms off-policy distillation and standard reinforcement learning. However, we find that its standard advantage weighted policy gradient suffers from three structural weaknesses, including high variance updates, vanishing gradients in zero-advantage regions, and exploration bottlenecks when corrective signals are insufficient. We therefore propose Asymmetric On-Policy Distillation (AOPD), which replaces ineffective negative reinforcement with localized divergence minimization in non-positive advantage regions while preserving positive reinforcement learning. Experiments on mathematical reasoning benchmarks show that AOPD consistently outperforms standard OPD, with average gains of 4.09 / 8.34 under strong / weak initialization, respectively. AOPD also maintains higher policy entropy during training and better capability retention during sequential tool-use adaptation.

Knowledge distillation improves large language model (LLM) reasoning by compressing the knowledge of a teacher LLM to train smaller LLMs. On-policy distillation advances this approach by having the student sample its own trajectories while a teacher LLM provides dense token-level supervision, addressing the distribution mismatch between training and inference in off-policy distillation methods. However, on-policy distillation typically requires a separate, often larger, teacher LLM and does not explicitly leverage ground-truth solutions available in reasoning datasets. Inspired by the intuition that a sufficiently capable LLM can rationalize external privileged reasoning traces and teach its weaker self (i.e., the version without access to privileged information), we introduce On-Policy Self-Distillation (OPSD), a framework where a single model acts as both teacher and student by conditioning on different contexts. The teacher policy conditions on privileged information (e.g., verified reasoning traces) while the student policy sees only the question; training minimizes the per-token divergence between these distributions over the student's own rollouts. We demonstrate the efficacy of our method on multiple mathematical reasoning benchmarks, achieving 4-8x token efficiency compared to reinforcement learning methods such as GRPO and superior performance over off-policy distillation methods.

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning capabilities of large language models on tasks such as mathematical reasoning and code generation. However, most RLVR methods assign a scalar outcome reward to an entire trajectory, resulting in sparse supervision and limited token-level credit assignment. On-policy distillation (OPD) provides denser supervision by distilling token-level distributions from a stronger teacher model, but requires an additional teacher and typically assumes a shared vocabulary. On-policy self-distillation (OPSD) removes this dependency by conditioning the same model on privileged information to construct a teacher policy. However, directly matching the teacher distribution may cause information leakage and unstable optimization. RLSD avoids direct matching by using the teacher signal only to modulate update magnitudes, but it cannot provide an explicit correction direction when the sampled reasoning fails. To address this tradeoff, we introduce H^{2}SD, a hybrid hindsight self distillation framework that uses the teacher differently according to trajectory correctness. For successful trajectories, the teacher receives the student response confirmed as correct together with a rephrasing instruction, and its probabilities on the original response tokens are used to modulate update magnitudes without changing the direction determined by the reward. For failed trajectories, we condition the teacher on a reference hint containing key reasoning steps and a verified answer, and minimize the reverse KL divergence from the student to the teacher. Experiments on multiple challenging reasoning benchmarks show that H^2SD consistently outperforms representative RLVR, OPSD, and RLSD baselines while maintaining stable optimization and favorable generation efficiency.

Consistency models have been proposed for fast generative modeling, achieving results competitive with diffusion and flow models. However, these methods exhibit inherent instability and limited reproducibility when training from scratch, motivating subsequent work to explain and stabilize these issues. While these efforts have provided valuable insights, the explanations remain fragmented, and the theoretical relationships remain unclear. In this work, we provide a theoretical examination of consistency models by analyzing them from a flow map-based perspective. This joint analysis clarifies how training stability and convergence behavior can give rise to degenerate solutions. Building on these insights, we revisit self-distillation as a practical remedy for certain forms of suboptimal convergence and reformulate it to avoid excessive gradient norms for stable optimization. We further demonstrate that our strategy extends beyond image generation to diffusion-based policy learning, without reliance on a pretrained diffusion model for initialization, thereby illustrating its broader applicability.

Bayesian optimization (BO) has contributed greatly to improving model performance by suggesting promising hyperparameter configurations iteratively based on observations from multiple training trials. However, only partial knowledge (i.e., the measured performances of trained models and their hyperparameter configurations) from previous trials is transferred. On the other hand, Self-Distillation (SD) only transfers partial knowledge learned by the task model itself. To fully leverage the various knowledge gained from all training trials, we propose the BOSS framework, which combines BO and SD. BOSS suggests promising hyperparameter configurations through BO and carefully selects pre-trained models from previous trials for SD, which are otherwise abandoned in the conventional BO process. BOSS achieves significantly better performance than both BO and SD in a wide range of tasks including general image classification, learning with noisy labels, semi-supervised learning, and medical image analysis tasks.

Knowledge distillation is classically a procedure where a neural network is trained on the output of another network along with the original targets in order to transfer knowledge between the architectures. The special case of self-distillation, where the network architectures are identical, has been observed to improve generalization accuracy. In this paper, we consider an iterative variant of self-distillation in a kernel regression setting, in which successive steps incorporate both model outputs and the ground-truth targets. This allows us to provide the first theoretical results on the importance of using the weighted ground-truth targets in self-distillation. Our focus is on fitting nonlinear functions to training data with a weighted mean square error objective function suitable for distillation, subject to ell_2 regularization of the model parameters. We show that any such function obtained with self-distillation can be calculated directly as a function of the initial fit, and that infinite distillation steps yields the same optimization problem as the original with amplified regularization. Furthermore, we provide a closed form solution for the optimal choice of weighting parameter at each step, and show how to efficiently estimate this weighting parameter for deep learning and significantly reduce the computational requirements compared to a grid search.

On-policy distillation is pivotal for transferring reasoning capabilities to capacity-constrained models, yet remains prone to instability and negative transfer. We show that on-policy distillation can be interpreted, both theoretically and empirically, as a form of policy optimization, where the teacher-student log-likelihood ratio acts as a token reward. From this insight, we introduce REOPOLD (Relaxed On-Policy Distillation) a framework that stabilizes optimization by relaxing the strict imitation constraints of standard on-policy distillation. Specifically, REOPOLD temperately and selectively leverages rewards from the teacher through mixture-based reward clipping, entropy-based token-level dynamic sampling, and a unified exploration-to-refinement training strategy. Empirically, REOPOLD surpasses its baselines with superior sample efficiency during training and enhanced test-time scaling at inference, across mathematical, visual, and agentic tool-use reasoning tasks. Specifically, REOPOLD outperforms recent RL approaches achieving 6.7~12x greater sample efficiency and enables a 7B student to match a 32B teacher in visual reasoning with a ~3.32x inference speedup.

Reasoning models have advanced rapidly, but the dominant reinforcement learning from verifiable rewards (RLVR) recipe remains surprisingly narrow: sample many responses and reward each with a single bit indicating whether the final answer is correct. Yet many settings provide rich feedback, including execution traces, tool outputs, expert corrections, and model self-evaluations. We study how to use such feedback through a distributional variant of the classic imitation learning algorithm DAgger, where the learner has local access to an expert distribution on states visited by the current policy. This yields a simple forward cross-entropy objective that admits a blackbox expert and whose sequence-level gradient {conduct rich credit assignment by propagating} future expert-student disagreement back to earlier decisions. We show that prior RL with self-distillation objectives based on reverse KL or Jensen-Shannon fail to guarantee monotonic policy improvement: even when the expert has higher reward, their updates may increase probability on worse actions. In contrast, we show that forward cross-entropy admits monotonic policy improvement and enjoys guarantees on regret. We further show that our objective optimizes a lower bound on teacher-weighted likelihood of success, leading to improved Pass@N. Empirically, our approach, DistIL, improves over RLVR and RL with self-distillation baselines across a variety of domains: scientific reasoning, coding, and solving hard mathematical problems.

Post-training for reasoning models typically combines supervised fine-tuning with reinforcement learning from verifiable rewards, most commonly with GRPO. However, this algorithm suffers from sparse rewards, limited exploration, and mode collapse. Building upon recent works on self-distillation, we propose Feedback Distillation, a training method where the model is trained to match, at the token level, its own distribution conditioned on privileged feedback produced by a language model. Feedback Distillation offers token-level supervision and can inject external knowledge. Evaluating our method for Lean4 theorem-proving, we find that Feedback Distillation maintains greater diversity in generated trajectories than GRPO, yielding higher policy entropy and better pass@k scaling. The two methods are complementary: initializing GRPO from a Feedback Distillation checkpoint outperforms either method alone. All in all, our results suggest a promising avenue to improve post-training for complex reasoning.

Self-distillation (SD) is the process of retraining a student on a mixture of ground-truth labels and the teacher's own predictions using the same architecture and training data. Although SD has been empirically shown to often improve generalization, its formal guarantees remain limited. We study SD for ridge regression in unconstrained setting in which the mixing weight ξ may be outside the unit interval. Conditioned on the training data and without any distributional assumptions, we prove that for any squared prediction risk (including out-of-distribution), the optimally mixed student strictly improves upon the ridge teacher for every regularization level λ> 0 at which the teacher ridge risk R(λ) is nonstationary (i.e., R'(λ) neq 0). We obtain a closed-form expression for the optimal mixing weight ξ^star(λ) for any value of λ and show that it obeys the sign rule: sign(ξ^star(λ))=-sign(R'(λ)). In particular, ξ^star(λ) can be negative, which is the case in over-regularized regimes. To quantify the risk improvement due to SD, we derive exact deterministic equivalents for the optimal SD risk in the proportional asymptotics regime (where the sample and feature sizes n and p both diverge but their aspect ratio p/n converges) under general anisotropic covariance and deterministic signals. Our asymptotic analysis extends standard second-order ridge deterministic equivalents to their fourth-order analogs using block linearization, which may be of independent interest. From a practical standpoint, we propose a consistent one-shot tuning method to estimate ξ^star without grid search, sample splitting, or refitting. Experiments on real-world datasets and pretrained neural network features support our theory and the one-shot tuning method.

Self-distillation enables language models to learn on-policy from their own trajectories by using the same model as both student and teacher, with the teacher being conditioned on privileged information unavailable to the student. Such information can come in different types or views, such as solutions, demonstrations, feedback, or final answers. This setup provides dense token-level feedback without relying on a separate external model, but creates a fundamental asymmetry: the teacher may rely on view-specific information that the student cannot access at inference time. Moreover, the best type of privileged information is often task-dependent, making it difficult to choose a single teacher view. In this work, we address both these challenges jointly by introducing AVSD (Adaptive-View Self-Distillation), a novel method of self-distillation with multiple privileged-information views, which reconstructs token-level supervision by separating stable cross-view consensus from view-specific residual signals. AVSD identifies the consensus signal shared across views, which provides a reliable update direction, and then selectively adds the view-specific residual signal to adjust the update magnitude when it both aligns with the consensus direction and remains proportionate to the consensus signal. Experiments on math competition benchmarks (AIME24, AIME25, and HMMT25) show that AVSD consistently outperforms both single-view self-distillation baselines and GRPO, achieving average Avg@8 gains of 3.1% and 2.2% over the strongest baselines on Qwen3-8B and Qwen3-4B, respectively. Moreover, on code-generation benchmarks (Codeforces, LiveCodeBench v6) using Qwen3-8B, AVSD outperforms the single-view self-distillation baseline by 2.4% on average.

Reinforcement learning for large language models faces a fundamental trade-off between sample efficiency and asymptotic performance: strictly on-policy methods discard trajectories after a single update, while off-policy reuse introduces distribution mismatch that existing trust-region techniques mitigate primarily by enforcing conservative optimization, often leaving rich training signals underutilized. To investigate this, we perform extensive off-policy updates on fixed data. Our experiments reveal that aggressive multi-step optimization brings rapid initial gains, but excessive updates cause trajectory probabilities to deviate and entropy to collapse, with performance plateauing early. Tightening KL constraints merely lowers the ceiling without resolving the degradation. This motivates Extreme Region Policy Distillation (ERPD), a two-stage framework that decouples sample efficiency from KL efficiency. The first stage performs weakly constrained off-policy optimization on fixed data to maximally extract training signals. The resulting policy provides token-level supervision. In the second stage, we distill these signals into the base policy under trust-region constraints, filtering harmful drift while preserving useful signals. The distilled policy achieves comparable or better performance with substantially smaller KL divergence, indicating that much of the first-stage divergence was spent on unnecessary drift rather than genuine improvement. Crucially, ERPD accommodates both strong and weak teachers: when aggressive optimization yields no stronger policy, even degenerate teachers provide effective supervision via alternative signal construction strategies. We validate ERPD on mathematical reasoning, showing gains for strong base models where on-policy training plateaus, and reliable improvements with weak teachers.

On-Policy Distillation (OPD) improves the learning efficiency of standard reinforcement learning through dense, token-level supervision from teachers. In the standard KL objective of OPD, token-level losses are uniformly averaged, implying equal weights for all tokens. However, we discover that not all tokens are created equal: as student rollouts grow longer, they deviate further from the teacher's distribution, leading to degraded supervision quality at later positions. As a result, OPD using only the first 30% of tokens can perform comparably to using all tokens, whereas OPD using only the last 30% of tokens barely learns anything. In this work, we provide a principled understanding of this issue through the lens of constrained optimization. Based on these insights, we derive Importance-Weighted On-Policy Distillation (IW-OPD), in which the weight assigned to each token depends on the accumulated discrepancy between the student's and teacher's distributions, naturally upweighting earlier tokens and downweighting later ones with larger deviations. We show that IW-OPD converges significantly faster than OPD, with better learning efficiency, and achieves better final performance than standard OPD in both same-size and cross-scale settings, improving performance up to 6.9 points on AIME-2025.

On-policy distillation (OPD) trains a student on its own trajectories with dense per-token supervision from a stronger teacher, and often outperforms off-policy distillation and standard reinforcement learning. However, we find that its effectiveness implicitly relies on two assumptions that frequently break in practice: trajectory-level alignment between the student and the teacher, and uniform token-level reliability of the teacher's preferences. We therefore propose Sign-Gated On-Policy Distillation (SG-OPD), which uses a binary verifier as a trust signal for the teacher at two complementary granularities: phased teacher sampling mixes in verifier-endorsed teacher rollouts at cold-start, and a sign-consistency gate extrapolates the distillation update on tokens where the teacher agrees with the verifier-correct direction and interpolates it where it disagrees. Experiments on competition-level mathematical reasoning benchmarks show that SG-OPD consistently outperforms standard OPD, with average gains of 1.98 and 7.50 at the per-sample and per-question levels, respectively.

On-policy self-distillation, where a student is pulled toward a copy of itself conditioned on privileged context (e.g., a verified solution or feedback), offers a promising direction for advancing reasoning capability without a stronger external teacher. Yet in math reasoning the gains are inconsistent, even when the same approach succeeds elsewhere. A pointwise mutual information analysis traces the failure to the privileged context itself: it inflates the teacher's confidence on tokens already implied by the solution (structural connectives, verifiable claims) and deflates it on deliberation tokens ("Wait", "Let", "Maybe") that drive multi-step search. We propose Anti-Self-Distillation (AntiSD), which ascends a divergence between student and teacher rather than descending it: this reverses the per-token sign and yields a naturally bounded advantage in one step. An entropy-triggered gate disables the term once the teacher entropy collapses, completing a drop-in replacement for default self-distillation. Across five models from 4B to 30B parameters on math reasoning benchmarks, AntiSD reaches the GRPO baseline's accuracy in 2 to 10x fewer training steps and improves final accuracy by up to 11.5 points. AntiSD opens a path to scalable self-improvement, where a language model bootstraps its own reasoning through its training signal.

We introduce a novel approach to large language model (LLM) distillation by formulating it as a constrained reinforcement learning problem. While recent work has begun exploring the integration of task-specific rewards into distillation processes, existing methods typically rely on ad-hoc reward weighting. We propose a principled optimization framework that maximizes task-specific rewards while constraining the divergence from the teacher model to remain below a specified threshold. Our approach adapts constrained state augmented reinforcement learning to the distillation setting, introducing a modified reward function that maintains theoretical guarantees of constraint satisfaction without requiring state augmentation or teacher model access during deployment and without the computational overhead of the dual Lagrangian methods. Through extensive experiments on mathematical reasoning tasks, we demonstrate that our method achieves better constraint satisfaction rates and better reasoning compared to the soft Lagrangian relaxation baselines while maintaining competitive task performance. Our framework provides a theoretically grounded and practically efficient solution for reward-aware distillation in resource-constrained settings.

On-policy distillation (OPD) has recently emerged as an important post-training paradigm. By using a stronger teacher model to provide dense, fine-grained supervision for sampled trajectories, OPD offers a clear advantage over reinforcement learning with verifiable rewards (RLVR), which typically depends on sparse binary or outcome-based environmental feedback. However, naive token-level distillation can suffer from gradient instability, due to magnitude misalignment in outlier states. To address this issue, we propose Globally Normalized Distillation Policy Optimization (GNDPO), a practical method that stabilizes optimization by transforming raw KL scores into batch-level relative advantages. This normalization effectively mitigates gradient explosions while retaining the benefits of token-level guidance. Experimental results show that GNDPO substantially improves training robustness and downstream performance across multimodal reasoning tasks. The code is released at https://github.com/OPPO-Mente-Lab/GNDPO.

On-policy self-distillation has become a strong recipe for LLM reasoning, where a privileged teacher supervises the student's own rollouts while conditioning on the reference solution. A design choice shared by nearly all such methods, however, has gone unquestioned: the teacher always sees the full reference reasoning. We argue that this default itself is part of the problem and identify a teacher-side exposure mismatch: when the teacher conditions on reasoning far beyond the student's current competence, the resulting token targets become too strong to absorb. A controlled fixed-exposure sweep makes this concrete on two fronts: 1) full exposure is not reliably the best choice, and 2) student-teacher mismatch grows monotonically as the teacher sees more privileged reasoning. This motivates treating teacher exposure not as a fixed hyperparameter but as a learnable training-time control variable. We therefore propose Adaptive Teacher Exposure for Self-Distillation (ATESD). ATESD models the reveal ratio with a lightweight Beta-policy controller conditioned on compact training-state statistics, and uses one sampled exposure for a short hold window of student updates. To make this exposure controller learnable, we optimize it with a discounted learning-progress reward that scores each held decision by its effect on the student's future improvement rather than its immediate loss change, addressing the delayed credit assignment induced by on-policy distillation. Experiments on AIME 24, AIME 25, and HMMT 25 across Qwen3-{1.7B, 4B, 8B} show that ATESD consistently outperforms competitive self-distillation and RL baselines, improving over OPSD by +0.95, +2.05, and +2.33 Average@12 points respectively, and establishing adaptive teacher exposure as an effective new axis for reasoning self-distillation.

On-policy distillation (OPD), which samples trajectories from the student model and supervises them with a teacher at the token level, avoids relying solely on verifiable terminal rewards and can yield better generalization than off-policy distillation. However, OPD requires expensive on-the-fly sampling of the student policy during training, which substantially increases training cost, especially for long responses. Our initial analysis shows that, during OPD, training signals are often concentrated in the prefix of each output, and that even a short teacher-generated prefix can significantly help the student produce the correct answer. Motivated by these observations, we propose a simple yet effective modification of OPD: we apply the distillation objective only to prefixes of student-generated outputs and terminate each sampling early during distillation. Experiments on a suite of AI-for-Math and out-of-domain benchmarks show that on-policy prefix distillation matches the performance of full OPD while reducing training FLOP by 2x-47x.

On-policy self-distillation (OPSD) trains a student on its own rollouts using a privileged teacher, but its standard objective weights all generated tokens equally, implicitly treating the privileged teacher target as equally reliable at every student-visited prefix. Existing entropy-based OPD methods relax this uniformity by modulating token-level supervision with teacher entropy, but high teacher entropy in reasoning has an ambiguous reliability meaning: it can reflect either non-viable uncertainty or benign solution diversity. To identify this phenomenon, we introduce a branch-viability diagnostic. Specifically, we record next-token alternatives from the privileged-answer teacher prompt, force each alternative after the student prompt plus its on-policy spine prefix, and test whether the resulting student-template continuation recovers the correct answer. On Qwen3-4B, we find that an oriented within-sequence position score is the strongest tested predictor of teacher-token reliability, reaching an area-under-ROC-curve (AUROC) of 0.83; local uncertainty scores are at most 0.57. Motivated by this trajectory-level structure, we propose Position-Weighted On-Policy Self-Distillation (PW-OPSD), which applies an increasing position weight while keeping the same student rollout, privileged teacher pass, and clipped forward-KL target as OPSD. In our comprehensive evaluations with different random seeds, the diagnostic-derived PW-OPSD improves AIME 2024 and AIME 2025 Avg@12 by +1.0 and +1.1 points, and a generalization evaluation on two larger-scale models from different families, DeepSeek-R1-Distill-Llama-8B and Olmo-3-7B-Think, also demonstrates consistent aggregate Avg@12 improvements. These results show that teacher-token reliability in reasoning distillation is trajectory-structured and can be utilized without additional teacher computation.

On-policy self-distillation (self-OPD) densifies reinforcement learning with verifiable rewards (RLVR) by letting a policy teach itself under privileged context. We find that when this guidance spans the full response, all-token KL spends gradients on mostly redundant positions and amplifies privileged-information leakage, causing entropy rise, shortened reasoning, and out-of-distribution degradation in long-horizon math training. We propose Token-Routed Alignment for Critical rEasoning (TRACE), which distills only on annotator-marked critical spans: forward KL on key spans of correct rollouts, optional reverse KL on localized error spans, and GRPO on all remaining tokens, with the KL channel annealed away after a short warm-up. Our analysis explains TRACE through two effects: forward KL provides non-vanishing lift to teacher-supported tokens that the student under-allocates, while span masking and decay keep cumulative privileged-gradient exposure finite. On four held-out math benchmarks plus GPQA-Diamond, TRACE improves over GRPO by 2.76 percentage points on average and preserves the Qwen3-8B base OOD score on GPQA-Diamond, where GRPO and all-token self-OPD baselines degrade. Gains persist under online self-annotation (+1.90 percentage points, about 69% of the strong-API gain), reducing the concern that TRACE merely imports external annotator capability. Across scales, the best routed action is base-dependent: on Qwen3-8B it is forward KL on key spans, while on Qwen3-1.7B it shifts to reverse KL on error spans.

Continual learning, enabling models to acquire new skills and knowledge without degrading existing capabilities, remains a fundamental challenge for foundation models. While on-policy reinforcement learning can reduce forgetting, it requires explicit reward functions that are often unavailable. Learning from expert demonstrations, the primary alternative, is dominated by supervised fine-tuning (SFT), which is inherently off-policy. We introduce Self-Distillation Fine-Tuning (SDFT), a simple method that enables on-policy learning directly from demonstrations. SDFT leverages in-context learning by using a demonstration-conditioned model as its own teacher, generating on-policy training signals that preserve prior capabilities while acquiring new skills. Across skill learning and knowledge acquisition tasks, SDFT consistently outperforms SFT, achieving higher new-task accuracy while substantially reducing catastrophic forgetting. In sequential learning experiments, SDFT enables a single model to accumulate multiple skills over time without performance regression, establishing on-policy distillation as a practical path to continual learning from demonstrations.

Reinforcement Learning has emerged as a post-training approach to elicit agentic RAG behaviors such as search and planning from language models. However, compact language models (e.g., 0.5B parameters) struggle due to poor reasoning ability, resulting in sparse rewards and unstable training. To overcome these difficulties, we propose Distillation-Guided Policy Optimization (DGPO), which addresses the challenges through cold-start initialization from teacher demonstrations and continuous teacher guidance during policy optimization. To systematically evaluate our approach, we introduce Agentic RAG Capabilities (ARC), a fine-grained metric analyzing reasoning, search coordination, and response synthesis. Comprehensive experiments demonstrate that DGPO enables compact models to achieve sophisticated agentic search behaviors, even outperforming the larger teacher model in some cases. DGPO makes agentic RAG feasible in computing resource-constrained environments.

On-policy distillation (OPD) has recently emerged as an effective post-training paradigm for consolidating the capabilities of specialized expert models into a single student model. Despite its empirical success, the conditions under which OPD yields reliable improvement remain poorly understood. In this work, we identify two fundamental bottlenecks that limit effective OPD: insufficient exploration of informative states and unreliable teacher supervision for student rollouts. Building on this insight, we propose Uni-OPD, a unified OPD framework that generalizes across Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs), centered on a dual-perspective optimization strategy. Specifically, from the student's perspective, we adopt two data balancing strategies to promote exploration of informative student-generated states during training. From the teacher's perspective, we show that reliable supervision hinges on whether aggregated token-level guidance remains order-consistent with the outcome reward. To this end, we develop an outcome-guided margin calibration mechanism to restore order consistency between correct and incorrect trajectories. We conduct extensive experiments on 5 domains and 16 benchmarks covering diverse settings, including single-teacher and multi-teacher distillation across LLMs and MLLMs, strong-to-weak distillation, and cross-modal distillation. Our results verify the effectiveness and versatility of Uni-OPD and provide practical insights into reliable OPD.

Training small language-model agents for long-horizon interactive tasks requires both fast imitation and reward-driven improvement. On-policy distillation (OPD) provides dense teacher guidance and typically improves rapidly in the early stage, but its gains saturate once the student approaches the teacher, limiting the final performance ceiling. Reinforcement learning (RL) directly optimizes environment rewards and encourages exploratory improvement toward a higher reward-defined ceiling, but sparse and delayed feedback makes early-stage learning much less efficient than OPD. In this paper, we propose ATOD (Annealed Turn-aware On-policy Distillation), a hybrid online distillation algorithm that explicitly exploits this complementarity. (1) ATOD uses an annealed OPD-RL schedule: OPD dominates early training to approach teacher-level behavior, while RL is gradually strengthened to drive reward-based exploration. (2) ATOD introduces Turn-level Disagreement-Uncertainty Reweighting (T-DUR), which softly amplifies high-utility turns and improves dense supervision in long trajectories. Experiments on ALFWorld, WebShop, and Search-QA show that ATOD consistently outperforms competing post-training baselines: across the three student sizes, ATOD improves average success rate by 3.03 points over OPD and 23.62 points over GRPO, while surpassing the corresponding teacher models by 2.16 points.

Current post-training methods in verifiable settings fall into two categories. Reinforcement learning (RLVR) relies on binary rewards, which are broadly applicable and powerful, but provide only sparse supervision during training. Distillation provides dense token-level supervision, typically obtained from an external teacher or using high-quality demonstrations. Collecting such supervision can be costly or unavailable. We propose Self-Distillation Zero (SD-Zero), a method that is substantially more training sample-efficient than RL and does not require an external teacher or high-quality demonstrations. SD-Zero trains a single model to play two roles: a Generator, which produces an initial response, and a Reviser, which conditions on that response and its binary reward to produce an improved response. We then perform on-policy self-distillation to distill the reviser into the generator, using the reviser's token distributions conditioned on the generator's response and its reward as supervision. In effect, SD-Zero trains the model to transform binary rewards into dense token-level self-supervision. On math and code reasoning benchmarks with Qwen3-4B-Instruct and Olmo-3-7B-Instruct, SD-Zero improves performance by at least 10% over the base models and outperforms strong baselines, including Rejection Fine-Tuning (RFT), GRPO, and Self-Distillation Fine-Tuning (SDFT), under the same question set and training sample budget. Extensive ablation studies show two novel characteristics of our proposed algorithm: (a) token-level self-localization, where the reviser can identify the key tokens that need to be revised in the generator's response based on reward, and (b) iterative self-evolution, where the improving ability to revise answers can be distilled back into generation performance with regular teacher synchronization.

Tool-integrated reasoning (TIR) is difficult to scale to small language models due to instability in long-horizon tool interactions and limited model capacity. While reinforcement learning methods like group relative policy optimization provide only sparse outcome-level rewards. Recently, on-policy distillation (OPD) has gained popularity by supplying dense token-level supervision from a teacher on student-generated trajectories. However, our experiments indicate that applying OPD to TIR leads to a critical failure mode: erroneous tool calls tend to cascade across subsequent reasoning steps, progressively amplifying student-teacher divergence and rendering the teacher's token-level supervision increasingly unreliable. To address this, we propose SOD, a step-wise on-policy distillation framework for small language model agents, which adaptively reweights distillation strength at each step based on step-level divergence. Therefore, SOD can attenuate potentially misleading teacher signals in high-divergence regions while preserving dense guidance in well-aligned states. Experiments on challenging math, science, and code benchmarks show that SOD achieves up to 20.86% improvement over the second-best baseline. Notably, our 0.6B student achieves 26.13% on AIME 2025, demonstrating effective transfer of agentic reasoning to lightweight models. Our code is available at https://github.com/YoungZ365/SOD.

On-policy self-distillation (OPSD) provides dense, token-level supervision for reasoning models by aligning a model's own distribution with the distribution it produces under privileged context, typically a verified solution. However, we show that the learning signal drawn from this distributional gap concentrates on style tokens rather than task-bearing ones, as the hinted model tends to produce more direct, shorter outputs. We term this pathology privilege-induced style drift, which destabilizes training or causes response length to shrink. To address this, we propose RLCSD (Reinforcement Learning with Contrastive on-policy Self-Distillation), which mitigates this drift by contrasting the teacher-student gap under a correct hint against that under a wrong hint, suppressing the style shift that conditioning on a hint tends to induce regardless of correctness, and yielding a signal that is more concentrated on task-bearing tokens. Experiments on Qwen3 (1.7B/4B/8B) and Olmo-3-7B-Think across mathematical and logical reasoning show that RLCSD consistently outperforms GRPO and prior OPSD methods. We further show that the contrastive principle is general: it plugs into existing OPSD methods to improve them, and its underlying insight extends to the broader cross-model on-policy distillation setting.

Context distillation enables language models to internalize in-context knowledge into their parameters. In our work, we propose On-Policy Context Distillation (OPCD), a framework that bridges on-policy distillation with context distillation by training a student model on its own generated trajectories while minimizing reverse Kullback-Leibler divergence against a context-conditioned teacher. We demonstrate the effectiveness of OPCD on two important applications: experiential knowledge distillation, where models extract and consolidate transferable knowledge from their historical solution traces, and system prompt distillation, where models internalize beneficial behaviors encoded in optimized prompts. Across mathematical reasoning, text-based games, and domain-specific tasks, OPCD consistently outperforms baseline methods, achieving higher task accuracy while better preserving out-of-distribution capabilities. We further show that OPCD enables effective cross-size distillation, where smaller student models can internalize experiential knowledge from larger teachers.

On-policy self-distillation has emerged as a promising paradigm for post-training language models, in which the model conditions on environment feedback to serve as its own teacher, providing dense token-level rewards without external teacher models or step-level annotations. Despite its empirical success, what this reward actually measures and what kind of credit it assigns remain unclear. Under a posterior-compatibility interpretation of feedback conditioning, standard in the implicit-reward literature, we show that the self-distillation token reward is a Bayesian filtering increment whose trajectory sum is exactly the pointwise mutual information between the response and the feedback given the input. This pMI can be raised by input-specific reasoning or by input-generic shortcuts, so we further decompose the teacher log-probability along the input axis. Based on this analysis, we propose CREDIT (Contrastive REward from DIsTillation), which isolates the input-specific component with a batch-contrastive baseline. At the sequence level, CREDIT is a teacher-side surrogate for a contrastive pMI objective that also penalizes responses remaining likely under unrelated inputs. Across coding, scientific reasoning, and tool-use benchmarks on two model families, CREDIT delivers the strongest aggregate performance at negligible additional compute.

In this work, we investigate the implicit regularization induced by teacher-student learning dynamics in self-distillation. To isolate its effect, we describe a simple experiment where we consider teachers at random initialization instead of trained teachers. Surprisingly, when distilling a student into such a random teacher, we observe that the resulting model and its representations already possess very interesting characteristics; (1) we observe a strong improvement of the distilled student over its teacher in terms of probing accuracy. (2) The learned representations are data-dependent and transferable between different tasks but deteriorate strongly if trained on random inputs. (3) The student checkpoint contains sparse subnetworks, so-called lottery tickets, and lies on the border of linear basins in the supervised loss landscape. These observations have interesting consequences for several important areas in machine learning: (1) Self-distillation can work solely based on the implicit regularization present in the gradient dynamics without relying on any dark knowledge, (2) self-supervised learning can learn features even in the absence of data augmentation and (3) training dynamics during the early phase of supervised training do not necessarily require label information. Finally, we shed light on an intriguing local property of the loss landscape: the process of feature learning is strongly amplified if the student is initialized closely to the teacher. These results raise interesting questions about the nature of the landscape that have remained unexplored so far. Code is available at https://github.com/safelix/dinopl.

Diffusion distillation, exemplified by Distribution Matching Distillation (DMD), has shown great promise in few-step generation but often sacrifices quality for sampling speed. While integrating Reinforcement Learning (RL) into distillation offers potential, a naive fusion of these two objectives relies on suboptimal raw sample evaluation. This sample-based scoring creates inherent conflicts with the distillation trajectory and produces unreliable rewards due to the noisy nature of early-stage generation. To overcome these limitations, we propose GDMD, a novel framework that redefines the reward mechanism by prioritizing distillation gradients over raw pixel outputs as the primary signal for optimization. By reinterpreting the DMD gradients as implicit target tensors, our framework enables existing reward models to directly evaluate the quality of distillation updates. This gradient-level guidance functions as an adaptive weighting that synchronizes the RL policy with the distillation objective, effectively neutralizing optimization divergence. Empirical results show that GDMD sets a new SOTA for few-step generation. Specifically, our 4-step models outperform the quality of their multi-step teacher and substantially exceed previous DMDR results in GenEval and human-preference metrics, exhibiting strong scalability potential.

On-policy self-distillation (OPSD) is promising as it removes the external teacher required by on-policy distillation (OPD), yet it still needs asymmetric information between teacher and student to ensure that the self-teacher provides a stronger learning signal than the student. Existing methods create this asymmetry either through privileged answers or visual evidence. We ask whether both can be removed, yielding a simpler form of OPSD driven purely by input conditioning. For this purpose, we propose Visual Contrastive Self-Distillation, namely VCSD, which converts image-content removal into an on-policy self-distillation signal. At each student-generated response prefix, the EMA teacher produces two next-token distributions under the same prompt and prefix -- one conditioned on the original image and the other on a content-erased control. Their token-wise log-probability difference highlights candidates whose likelihood is specifically increased by the instance-level visual content. We use this contrast to sharpen the teacher's original-image distribution within its plausible support, and distill the resulting full-distribution target into the student. Using ViRL39K dataset, VCSD consistently outperforms matched OPSD across Qwen3-VL and Qwen3.5 models. For example, on Qwen3-VL, it improves the seven-benchmark aggregate from 62.27% rightarrow 67.04% at 2B, 71.30% rightarrow 73.16% at 4B, and 72.51% rightarrow 76.26% at 8B. Furthermore, VCSD requires no external teacher, privileged answers, visual evidence signals, reasoning traces, or additional inference-time cost.

Self-distillation (SD) offers a promising path for adapting large language models (LLMs) without relying on stronger external teachers. However, SD in autoregressive LLMs remains challenging because self-generated trajectories are free-form, correctness is task-dependent, and plausible rationales can still provide unstable or unreliable supervision. Existing methods mainly examine isolated design choices, leaving their effectiveness, roles, and interactions unclear. In this paper, we propose UniSD, a unified framework to systematically study self-distillation. UniSD integrates complementary mechanisms that address supervision reliability, representation alignment, and training stability, including multi-teacher agreement, EMA teacher stabilization, token-level contrastive learning, feature matching, and divergence clipping. Across six benchmarks and six models from three model families, UniSD reveals when self-distillation improves over static imitation, which components drive the gains, and how these components interact across tasks. Guided by these insights, we construct UniSDfull, an integrated pipeline that combines complementary components and achieves the strongest overall performance, improving over the base model by +5.4 points and the strongest baseline by +2.8 points. Extensive evaluation highlights self-distillation as a practical and steerable approach for efficient LLM adaptation without stronger external teachers.

On-policy distillation (OPD), which aligns the student with the teacher's logit distribution on student-generated trajectories, has demonstrated strong empirical gains in improving student performance and often outperforms off-policy distillation and reinforcement learning (RL) paradigms. In this work, we first theoretically show that OPD is a special case of dense KL-constrained RL where the reward function and the KL regularization are always weighted equally and the reference model can by any model. Then, we propose the Generalized On-Policy Distillation (G-OPD) framework, which extends the standard OPD objective by introducing a flexible reference model and a reward scaling factor that controls the relative weight of the reward term against the KL regularization. Through comprehensive experiments on math reasoning and code generation tasks, we derive two novel insights: (1) Setting the reward scaling factor to be greater than 1 (i.e., reward extrapolation), which we term ExOPD, consistently improves over standard OPD across a range of teacher-student size pairings. In particular, in the setting where we merge the knowledge from different domain experts, obtained by applying domain-specific RL to the same student model, back into the original student, ExOPD enables the student to even surpass the teacher's performance boundary and outperform the domain teachers. (2) Building on ExOPD, we further find that in the strong-to-weak distillation setting (i.e., distilling a smaller student from a larger teacher), performing reward correction by choosing the reference model as the teacher's base model before RL yields a more accurate reward signal and further improves distillation performance. However, this choice assumes access to the teacher's pre-RL variant and incurs more computational overhead. We hope our work offers new insights for future research on OPD.

On-policy distillation (OPD) has become a central post-training tool for large language models (LLMs), providing dense per-token teacher supervision along the student's own rollouts. In this work, we identify a common structural cause underlying OPD, which we call prefix failure. Under prefix failure, dense per-token supervision induces a bimodal teacher mixture and fragmented gradients that token-level loss truncation or reweighting fail to address. This observation motivates us to move beyond token-level loss interventions toward trajectory-level output corrections. We thus propose Trajectory-Refined Distillation (TRD), a trajectory-level correction method that revises the student's rollout under the teacher guidance while within on-policy support. By correcting problematic prefixes before distillation, TRD mitigates prefix failure at its source. Moreover, TRD improves the exploration by exposing the student to alternative valid derivations under teacher guidance, even when the original rolls are already correct. TRD can also be applied to on-policy self-distillation (OPSD), a parameter-sharing variant that uses the student model conditioned on privileged informations as the teacher. Across a wide range of benchmarks and base models at multiple scales, TRD consistently outperforms prior baselines, improving single-attempt accuracy and broadening reasoning coverage. Code is available at https://github.com/louieworth/trd

We study on-policy distillation (OPD) for agentic tasks, where an LLM agent interacts with an environment over multiple turns and a student imitates a teacher over these multi-turn interaction histories. Fully online OPD is costly because each update requires fresh student rollouts through the environment and teacher queries at visited histories. We propose Replayed-Prefix On-Policy Distillation (ReOPD), an off-environment alternative that reuses pre-collected teacher trajectories as replayed prefixes: the student acts at selected steps, while the teacher provides dense per-step supervision without executing new environment interactions. We show that multi-turn OPD introduces a prefix trap: making histories more student-on-policy improves relevance to the student, but can query the teacher on histories where its target is unreliable. This creates a two-sided distribution shift between student occupancy and teacher reliability. ReOPD addresses this by treating multi-turn OPD as a reliability-aware prefix distribution design and implements it with a simple step-decaying sampling schedule that emphasizes early, lower-shift prefixes. Across mathematical reasoning with Python and search environments over multiple teacher and student model scales, ReOPD preserves or improves OPD-level accuracy, uses zero tool calls during student training, and is at least 4times faster per rollout than OPD. ReOPD therefore turns expensive agent-environment interaction into a reusable offline resource, enabling scalable distillation across tools, tasks, and environments.

On-policy distillation (OPD) has become a promising paradigm for reasoning-oriented post-training of large language models (LLMs), especially when combined with reinforcement learning from verifiable rewards (RLVR). Existing OPD methods rely on reverse KL (RKL)-based teacher supervision over trajectories sampled from the student policy. However, we identify a critical limitation: under large teacher--student policy divergence, RL-driven exploration often produces trajectories outside the teacher distribution, resulting in uninformative negative feedback. To address this, we propose Teacher-Guided Policy Optimization (TGPO), an on-policy reasoning distillation method that remains effective under large policy divergence settings. Rather than relying solely on evaluative supervision, TGPO uses teacher to directly guide token level generation conditioning on student-generated contexts; together with RLVR-style trajectory level rewards, TGPO steers exploration toward improved continuations. Experiments on reasoning benchmarks show that TGPO consistently outperforms existing RKL-based OPD methods and remains robust across different teacher models.

Knowledge distillation (KD) is a powerful paradigm for compressing large language models (LLMs), whose effectiveness depends on intertwined choices of divergence direction, optimization strategy, and data regime. We break down the design of existing KD methods and present a unified view that establishes connections between them, reformulating KD as a reweighted log-likelihood objective at the token level. We further propose Hybrid Policy Distillation (HPD), which integrates the complementary advantages of forward and reverse KL to balance mode coverage and mode-seeking, and combines off-policy data with lightweight, approximate on-policy sampling. We validate HPD on long-generation math reasoning as well as short-generation dialogue and code tasks, demonstrating improved optimization stability, computational efficiency, and final performance across diverse model families and scales. The code related to this work is available at https://github.com/zwhong714/Hybrid-Policy-Distillation.

Self-Distillation is a special type of knowledge distillation where the student model has the same architecture as the teacher model. Despite using the same architecture and the same training data, self-distillation has been empirically observed to improve performance, especially when applied repeatedly. For such a process, there is a fundamental question of interest: How much gain is possible by applying multiple steps of self-distillation? To investigate this relative gain, we propose studying the simple but canonical task of linear regression. Our analysis shows that the excess risk achieved by multi-step self-distillation can significantly improve upon a single step of self-distillation, reducing the excess risk by a factor as large as d, where d is the input dimension. Empirical results on regression tasks from the UCI repository show a reduction in the learnt model's risk (MSE) by up to 47%.

Reinforcement learning (RL) post-training has recently driven major gains in long chain-of-thought reasoning large language models (LLMs), but the high inference cost of such models motivates distillation into smaller students. Most existing knowledge distillation (KD) methods are designed for supervised fine-tuning (SFT), relying on fixed teacher traces or teacher-student Kullback-Leibler (KL) divergence-based regularization. When combined with RL, these approaches often suffer from distribution mismatch and objective interference: teacher supervision may not align with the student's evolving rollout distribution, and the KL regularizer can compete with reward maximization and require careful loss balancing. To address these issues, we propose RL-aware distillation (RLAD), which performs selective imitation during RL -- guiding the student toward the teacher only when it improves the current policy update. Our core component, Trust Region Ratio Distillation (TRRD), replaces the teacher-student KL regularizer with a PPO/GRPO-style likelihood-ratio objective anchored to a teacher--old-policy mixture, yielding advantage-aware, trust-region-bounded distillation on student rollouts and naturally balancing exploration, exploitation, and imitation. Across diverse logic reasoning and math benchmarks, RLAD consistently outperforms offline distillation, standard GRPO, and KL-based on-policy teacher-student knowledge distillation.

On-Policy Distillation (OPD) is a fundamental technique for efficient post-training of large language models (LLMs), with broad applications in agent learning, multi-task enhancement, and model compression. However, OPD training becomes unstable when the teacher and student distributions differ substantially, as teacher supervision on student-generated tokens may yield unreliable policy gradients and even cause optimization failure. This work addresses reliable on-policy token-level supervision through credit assignment strategies, and proposes Trust Region On-Policy Distillation, TrOPD. It features the following characteristics: 1) Trust-Region On-Policy Learning: TrOPD performs OPD only in regions where the teacher provides reliable supervision, mitigating the optimization difficulty of the K1 reverse-KL estimator under distribution mismatch. 2) Outlier Estimation: For outlier regions, we explore gradient clipping, masking, and forward-KL estimation to reduce the adverse effects of unreliable supervision. 3) Off-Policy Guidance: The student continues generation from teacher prefixes and uses forward KL to imitate off-policy guidance, encouraging on-policy exploration toward reliable regions. Experiments show that TrOPD consistently outperforms SoTA OPD baselines, including OPD, EOPD, and REOPOLD, across mathematical reasoning, code generation, and general-domain benchmarks.

Diffusion models achieve remarkable generation quality but suffer from computational intensive sampling due to suboptimal step discretization. While existing works focus on optimizing denoising directions, we address the principled design of stepsize schedules. This paper proposes Optimal Stepsize Distillation, a dynamic programming framework that extracts theoretically optimal schedules by distilling knowledge from reference trajectories. By reformulating stepsize optimization as recursive error minimization, our method guarantees global discretization bounds through optimal substructure exploitation. Crucially, the distilled schedules demonstrate strong robustness across architectures, ODE solvers, and noise schedules. Experiments show 10x accelerated text-to-image generation while preserving 99.4% performance on GenEval. Our code is available at https://github.com/bebebe666/OptimalSteps.

On-policy distillation (OPD) is an increasingly important paradigm for post-training language models. However, we identify a pervasive Scaling Law of Miscalibration: while OPD effectively improves task accuracy, it systematically traps models in severe overconfidence. We trace this failure to an information mismatch: teacher supervision is formed under privileged context available during training, whereas the deployed model must report confidence using only deployment-time information. We formalize this perspective theoretically, showing that teacher-conditioned success is generally not a valid target for deployment-time confidence and that helpful privileged context induces entropy collapse and a systematic optimism bias. To address this, we propose a calibration-aware OPD framework, CaOPD, that estimates empirical confidence from model rollouts, replaces self-reported confidence with this student-grounded target, and distills the revised response through the same self-distillation pipeline. Experiments across various models and domains show that CaOPD achieves Pareto-optimal calibration while maintaining competitive capability, generalizing robustly under out-of-distribution and continual learning. Our findings highlight that capability distillation does not imply calibrated confidence, and that confidence should be treated as an essential objective in post-training. Code: https://github.com/SalesforceAIResearch/CaOPD

On-policy distillation (OPD) trains a student on its own trajectories under token-level teacher supervision, but existing methods are capped by a single-teacher capability ceiling: when the teacher errs, the student inherits the error. OPD also remains largely unexplored in agentic tasks, where per-step errors compound across long trajectories and destabilize training. We propose MAD-OPD (Multi-Agent Debate-driven On-Policy Distillation), which breaks this ceiling by recasting the distillation teacher as a deliberative collective of teachers that debate over the student's on-policy state; the debate produces an emergent collective intelligence that supplies token-level supervision, with each teacher's contribution weighted by its post-debate confidence. To extend OPD to agentic tasks, we also introduce On-Policy Agentic Distillation (OPAD), which adds step-level sampling to stabilize training under multi-step error compounding. We additionally derive a task-adaptive divergence principle, selecting JSD (Jensen-Shannon divergence) for agentic stability and reverse KL (Kullback-Leibler) divergence for code generation, and verify it both theoretically and empirically. Across six teacher-student configurations (Qwen3 and Qwen3.5; 1.7B-14B students, 8B-32B teachers) and five agentic and code benchmarks, MAD-OPD ranks first across all six configurations; on the 14B+8Bto4B setting it lifts the agentic average by +2.4% and the code average by +3.7% over the stronger single-teacher OPD.

Reinforcement learning with verifiable rewards (RLVR) commonly uses entropy for advantage shaping. However, entropy cannot distinguish useful uncertainty from detrimental confusion, limiting its effectiveness as a correctness signal. We propose Contrastive Policy Optimization (CPO), which uses token-level contrastive disagreement between reference-guided and vanilla generation distributions for correctness-aware advantage shaping. Both theoretical and empirical results show that this disagreement reliably indicates token-level correctness. We further show that On-policy Distillation is a special case of CPO, where the posterior distribution is instantiated by an external teacher model. CPO also resolves the zero-advantage problem. Experiments on in-domain and out-of-domain benchmarks demonstrate that CPO substantially outperforms entropy-based RLVR methods while maintaining strong generalization. Further analysis shows that correct and incorrect responses naturally support exploration and exploitation respectively, and balancing both leads to the best performance.

Distribution Matching Distillation (DMD) distills a pre-trained multi-step diffusion model to a few-step one to improve inference efficiency. However, the performance of the latter is often capped by the former. To circumvent this dilemma, we propose DMDR, a novel framework that combines Reinforcement Learning (RL) techniques into the distillation process. We show that for the RL of the few-step generator, the DMD loss itself is a more effective regularization compared to the traditional ones. In turn, RL can help to guide the mode coverage process in DMD more effectively. These allow us to unlock the capacity of the few-step generator by conducting distillation and RL simultaneously. Meanwhile, we design the dynamic distribution guidance and dynamic renoise sampling training strategies to improve the initial distillation process. The experiments demonstrate that DMDR can achieve leading visual quality, prompt coherence among few-step methods, and even exhibit performance that exceeds the multi-step teacher.

On-Policy Distillation (OPD) has emerged as a dominant post-training paradigm for large language models, especially for reasoning domains. However, OPD remains unstable in practice due to the high gradient variance of its single-sample Monte Carlo estimator, and recipes for stable training are still immature. We propose vOPD (On-Policy Distillation with a control variate baseline), which casts OPD as policy-gradient RL and stabilizes it by introducing a control variate baseline-canonically a value function -- from the RL literature. We show that the OPD value function admits a closed form as the per-token negative reverse KL divergence between the student and the teacher, available directly from the already-computed forward pass with no additional critic or inference. Existing stabilization methods either compute the full token-level reverse KL over the entire vocabulary, adding significant overhead, or restrict it to a top-k support, biasing the objective. vOPD instead preserves the lightweight single-sample estimator, subtracting the value function as a detached baseline to keep the gradient unbiased while reducing variance. Furthermore, we show that a top-k approximation of the baseline further lowers cost without compromising performance. Across mathematical and scientific reasoning benchmarks, vOPD consistently outperforms vanilla OPD and matches the most expensive full-vocabulary baseline, offering an efficient stabilization of On-Policy Distillation through principled RL variance reduction.

Differentiable Architecture Search (DARTS) is a simple yet efficient Neural Architecture Search (NAS) method. During the search stage, DARTS trains a supernet by jointly optimizing architecture parameters and network parameters. During the evaluation stage, DARTS discretizes the supernet to derive the optimal architecture based on architecture parameters. However, recent research has shown that during the training process, the supernet tends to converge towards sharp minima rather than flat minima. This is evidenced by the higher sharpness of the loss landscape of the supernet, which ultimately leads to a performance gap between the supernet and the optimal architecture. In this paper, we propose Self-Distillation Differentiable Neural Architecture Search (SD-DARTS) to alleviate the discretization gap. We utilize self-distillation to distill knowledge from previous steps of the supernet to guide its training in the current step, effectively reducing the sharpness of the supernet's loss and bridging the performance gap between the supernet and the optimal architecture. Furthermore, we introduce the concept of voting teachers, where multiple previous supernets are selected as teachers, and their output probabilities are aggregated through voting to obtain the final teacher prediction. Experimental results on real datasets demonstrate the advantages of our novel self-distillation-based NAS method compared to state-of-the-art alternatives.

Self-distillation (SD) is the process of first training a teacher model and then using its predictions to train a student model with the same architecture. Specifically, the student's objective function is big(xi*ell(teacher's predictions, student's predictions) + (1-xi)*ell(given labels, student's predictions)big), where ell is some loss function and xi is some parameter in [0,1]. Empirically, SD has been observed to provide performance gains in several settings. In this paper, we theoretically characterize the effect of SD in two supervised learning problems with noisy labels. We first analyze SD for regularized linear regression and show that in the high label noise regime, the optimal value of xi that minimizes the expected error in estimating the ground truth parameter is surprisingly greater than 1. Empirically, we show that xi > 1 works better than xi leq 1 even with the cross-entropy loss for several classification datasets when 50\% or 30\% of the labels are corrupted. Further, we quantify when optimal SD is better than optimal regularization. Next, we analyze SD in the case of logistic regression for binary classification with random label corruption and quantify the range of label corruption in which the student outperforms the teacher in terms of accuracy. To our knowledge, this is the first result of its kind for the cross-entropy loss.

On-policy distillation (OPD) is increasingly used to improve large language model reasoning, but its training dynamics remain poorly understood. We characterize the trajectory of OPD updates in parameter space and compare it with supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR). A suite of parameter-space diagnostics consistently places OPD in a relaxed off-principal regime: compared with SFT, its updates affect fewer weights and avoid principal directions more strongly, while compared with RLVR, they remain less tightly constrained. Beyond this static localization, OPD exhibits subspace locking: its cumulative updates rapidly enter a narrow low-dimensional channel. Constraining training to the update subspace formed early in training preserves OPD performance but substantially degrades SFT, indicating that the locked subspace is functionally sufficient for OPD. Control experiments further show that sparsifying the update tokens and shifting rollout generation off-policy preserve the rank dynamics, whereas mixing the OPD objective with RLVR changes them. Overall, these results suggest that OPD is not merely an intermediate point between SFT and RLVR, but induces its own update geometry in parameter space.

Reinforcement learning (RL) can be used to improve the policy (denoiser) of diffusion large language models (dLLMs), while being hindered by the intractability of the policy likelihood. A dominant and efficient family of methods replaces the likelihood in standard RL with its evidence lower bound (ELBO), estimated from randomly masked sequences. Despite being well aligned with pre-training, these approaches introduce bias through training--inference mismatch by using the ELBO as a likelihood surrogate, which can degrade performance. In this work, we propose Guided Denoiser Self-Distillation (GDSD) to directly distill the denoiser of dLLMs from an advantage-guided self-teacher, derived from the closed-form optimum of reverse-KL regularized RL. GDSD matches the dLLM's denoiser logits to the teacher's via a normalization-free objective, which reduces RL to likelihood-free self-distillation and thus bypasses the TIM biases. Recent ELBO-based methods emerge as instances of applying different distillation divergences, but with diagnosable pathologies that GDSD avoids. On planning, math, and coding benchmarks with LLaDA-8B and Dream-7B, GDSD consistently outperforms prior state-of-the-art ELBO-based methods with a more stable training reward dynamics, achieving test-accuracy improvements of up to +19.6%. These results suggest that direct denoiser self-distillation, without relying on an ELBO likelihood surrogate, can provide a more stable and effective RL procedure for dLLMs. Code is available at https://github.com/GaryBall/GDSD.

On-policy distillation is an alternative post-training method in reinforcement learning that alleviates the constraints imposed by reward models by providing token-level supervision from a teacher model. Although on-policy distillation has been studied and applied across various settings, its fundamental design remains underexplored. In this paper, we introduce a new distillation reward, termed the delta signal, instead of directly imitating the teacher's output distribution. The delta signal is defined as the difference between the teacher model and its base model prior to instruction tuning for reasoning capability. It therefore captures the changes induced by reasoning tuning and provides a more direct signal for transferring reasoning capabilities. Using extensive empirical evidence, we show that the delta signal substantially improves on-policy distillation and refer to the new distillation method as On-Policy Delta Distillation (OPD^2). Experiments across mathematics, science, and code-reasoning benchmarks demonstrate that OPD^2 consistently outperforms conventional on-policy distillation, enabling reasoning LLMs to achieve strong performance with only a short post-training period. Code will be available at https://github.com/naver-ai/opd2

We introduce ORPO-Distill, a general-purpose method for cross-architecture LLM distillation that formulates the problem as a preference optimization task. Unlike standard CoT distillation, the approach transfers knowledge through diverse reasoning traces. It employs an Odds-Ratio Preference Optimization objective that contrasts teacher and student traces for more effective learning, and adopts a mixed-policy strategy for utilizing student-generated outputs, outperforming both off- and on-policy alternatives. Experiments on five datasets and multiple student models show consistent improvements over conventional black-box KD baselines.

On-policy distillation (OPD) trains student models under their own induced distribution while leveraging supervision from stronger teachers. We identify a failure mode of OPD: as training progresses, on-policy rollouts can undergo abrupt length inflation, causing truncated trajectories to dominate the training data. This truncation collapse coincides with abrupt repetition saturation and induces biased gradient signals, leading to severe training instability and sharp degradation in validation performance. We attribute this problem to the interaction between student-induced data collection and the distillation objective, which implicitly favors long and repetitive rollouts. To address this issue, we propose StableOPD, a stabilized OPD framework that combines a reference-based divergence constraint with rollout mixture distillation. These together mitigate repetition-induced length inflation and further stabilize OPD training. Across multiple math reasoning datasets, our approach prevents truncation collapse, stabilizes training dynamics, and improves performance by 7.2% on average.

The landscape of high-performance image generation models is currently shifting from the inefficient multi-step ones to the efficient few-step counterparts (e.g, Z-Image-Turbo and FLUX.2-klein). However, these models present significant challenges for directly continuous supervised fine-tuning. For example, applying the commonly used fine-tuning technique would compromises their inherent few-step inference capability. To address this, we propose D-OPSD, a novel training paradigm for step-distilled diffusion models that enables on-policy learning during supervised fine-tuning. We first find that the modern diffusion model where the LLM/VLM serves as the encoder can inherit its encoder's in-context capabilities. This enables us to make the training as an on-policy self-distillation process. Specifically, during training, we make the model acts as both the teacher and the student with different contexts, where the student is conditioned only on the text feature, while the teacher is conditioned on the multimodal feature of both the text prompt and the target image. Training minimizes the two predicted distributions over the student's own roll-outs. By optimized on the model's own trajectory and under it's own supervision, D-OPSD enables the model to learn new concept, style, etc. without sacrificing the original few-step capacity.

Reinforcement learning for multi-turn agents suffers from a credit-assignment mismatch: rewards are sparse and trajectory-level, while success often hinges on a few local decisions. Existing online policy distillation (OPD) provides denser token-level supervision, but typically treats heterogeneous agent trajectories as monolithic strings rather than causal interaction units. We present StepOPSD, a post-rollout preference self-distillation framework that takes the agent step as the unit of credit redistribution. StepOPSD decomposes trajectories into action-centered step segments, rescoring them under hindsight-enriched teacher contexts and converting token-level log-probability gaps into sign-preserving advantage shaping with a normalized per-step credit budget before the GRPO update. Across ALFWorld and Search-QA with Qwen3-1.7B and Qwen2.5-3B-Instruct, StepOPSD attains best or second-best results on subsets most sensitive to local causal errors, including first-place performance on ALFWorld Heat (79.1%), PickTwo (95.0%), Search-QA TriviaQA (61.6%), and tied-best performance on HotpotQA (40.4%). The results further reveal a consistent two-knob law: smaller α_clip acts as a broadly stabilizing local trust region, whereas the optimal global mixing strength λ_mix remains task-dependent. These findings suggest that step-aware distillation is most useful when trajectory-level rewards are weakly aligned with the local action that determines downstream success.

On-policy distillation offers dense, per-token supervision for training reasoning models; however, it remains unclear under which conditions this signal is beneficial and under which it is detrimental. Which teacher model should be used, and in the case of self-distillation, which specific context should serve as the supervisory signal? Does the optimal choice vary from one token to the next? At present, addressing these questions typically requires costly training runs whose aggregate performance metrics obscure the dynamics at the level of individual tokens. We introduce a training-free diagnostic framework that operates at the highest resolution: per token, per question, and per teacher. We derive an ideal per-node gradient defined as the parameter update that maximally increases the student's probability of success. We then develop a scalable targeted-rollout algorithm to estimate this gradient efficiently, even for long chains of intermediate thoughts. The gradient alignment score, defined as the cosine similarity between this ideal gradient and any given distillation gradient, quantifies the extent to which a particular configuration approximates the ideal signal. Across a range of self-distillation settings and external teacher models, we observe that distillation guidance exhibits substantially higher alignment with the ideal on incorrect rollouts than on correct ones, where the student already performs well and the teacher's signal tends to become noisy. Furthermore, we find that the optimal distillation context depends jointly on the student model's capacity and the target task, and that no single universally effective configuration emerges. These findings motivate the use of per-task, per-token diagnostic analyses for distillation.

Knowledge distillation is central to LLM post-training, yet its design space remains poorly understood, especially alongside reinforcement learning (RL). We show that the prevailing paradigms, off-policy distillation and on-policy distillation (OPD), implicitly couple two orthogonal choices: prefix source and token-level KL direction. This follows from decomposing sequence-level KL over autoregressive response distributions: forward KL pairs teacher prefixes with token-level forward KL, and reverse KL pairs student prefixes with token-level reverse KL. We argue this coupling is not intrinsic: decoupling the two axes yields four valid objectives. We establish gradient-level identities showing forward KL gives SFT-style cross-entropy matching with teacher soft targets, whereas reverse KL gives an RL-style policy-gradient objective with a dense teacher-student log-ratio reward, connecting them to off-policy SFT, DAgger-style on-policy SFT, offline-RL-style distillation, and OPD. We conduct an extensive controlled study on math reasoning, evaluating the four objectives both as standalone methods and as initializations for subsequent RL. The results reveal three tradeoffs: KL direction induces an accuracy-entropy tradeoff, prefix source a quality-compute tradeoff, and training length an accuracy-stability tradeoff. Motivated by these findings, we propose KL mixing and an entropy-gated length curriculum. KL mixing shows long-sequence distillation requires substantial forward-KL weight to prevent entropy collapse and length inflation without sacrificing accuracy. The entropy-gated length curriculum improves Avg@k and Pass@k by 3.6 and up to 5.8 points, and cuts average response length by roughly 3x versus fixed long-horizon training. Our results provide a framework and practical methods for designing reasoning distillation objectives that balance accuracy, diversity, compute, and RL behavior.

We propose Algorithm Distillation (AD), a method for distilling reinforcement learning (RL) algorithms into neural networks by modeling their training histories with a causal sequence model. Algorithm Distillation treats learning to reinforcement learn as an across-episode sequential prediction problem. A dataset of learning histories is generated by a source RL algorithm, and then a causal transformer is trained by autoregressively predicting actions given their preceding learning histories as context. Unlike sequential policy prediction architectures that distill post-learning or expert sequences, AD is able to improve its policy entirely in-context without updating its network parameters. We demonstrate that AD can reinforcement learn in-context in a variety of environments with sparse rewards, combinatorial task structure, and pixel-based observations, and find that AD learns a more data-efficient RL algorithm than the one that generated the source data.

Knowledge distillation (KD) has shown great promise in transferring knowledge from larger teacher models to smaller student models. However, existing KD strategies for large language models often minimize output distributions between student and teacher models indiscriminately for each token. This overlooks the imbalanced nature of tokens and their varying transfer difficulties. In response, we propose a distillation strategy called Self-Evolution KD. The core of this approach involves dynamically integrating teacher distribution and one-hot distribution of ground truth into the student distribution as prior knowledge, which promotes the distillation process. It adjusts the ratio of prior knowledge based on token learning difficulty, fully leveraging the teacher model's potential. Experimental results show our method brings an average improvement of approximately 1.4 SacreBLEU points across four translation directions in the WMT22 test sets. Further analysis indicates that the improvement comes from better knowledge transfer from teachers, confirming our hypothesis.

Conditioning a language model on additional context, such as feedback on a previous attempt, typically improves its response. Self-distillation trains the model to retain this improvement when the context is not present. The method works by matching the model's output distribution under two settings: a student that sees only the question, and a self-teacher that also sees the context. What the model learns therefore depends on what context the self-teacher receives, yet the design of this context remains largely unexplored. We study context design for self-distillation by training a solver on feedback from a frozen critic. We compare three conditions: (i) a binary reward (GRPO), (ii) the reference solution, and (iii) a step-by-step critique aligned to the solver's reasoning trace. Step-aligned critique yields the largest gains, outperforming GRPO by 16.11 points and reference-solution-conditioned self-distillation by 5.27 points (Avg@12). Per-token advantage analysis reveals why: step-aligned feedback targets only the tokens where reasoning fails, leaving correct behavior intact. Conditioning on the reference solution, by contrast, pressures the model to change its behavior at every token (even correct steps) because an alternative derivation inevitably differs in phrasing and approach. This suggests that structural alignment between feedback and the solver's reasoning is a key driver of self-distillation effectiveness.

Reinforcement Learning with Verifiable Rewards (RLVR) enhances Large Language Model (LLM) reasoning but suffers from advantage collapse on ``hard samples'' where all rollouts fail. This lack of variance eliminates crucial learning signals. For these intractable samples, simply scaling up rollout budgets offers limited gains. We introduce Joint Policy and Prompt Optimization (P^2O) to mitigate this collapse by alternating continuous policy updates with discrete prompt evolution. P^2O leverages the GEPA algorithm to discover successful reasoning prompts for intractable instances. Via context distillation, the model internalizes these prompt-induced gains directly into its parameters, removing the need for inference-time prompting. Empirically, P^2O restores critical advantage signals, significantly outperforming standard GRPO and surpassing baselines with doubled rollout budgets, ultimately yielding strong out-of-distribution generalization and an up to 9.5% performance improvement. Our findings expose the limits of standard exploration in sparse-reward environments, illuminating the potential of unifying evolutionary algorithms with reinforcement learning. This integration of discrete semantic search and continuous parameter updates establishes a self-reinforcing paradigm for autonomous LLM alignment.

Scaling on-policy distillation (OPD) for large language models (LLMs) confronts a fundamental tension: asynchronous execution is necessary for system efficiency, but structurally deviates from the ideal on-policy objective. To address this challenge, we theoretically decompose the objective discrepancy into rollout drift and supervision drift, capturing staleness in student rollout and teacher context, respectively. Building on this, we introduce a sample-level freshness score that quantifies the reliability of a buffered sample with respect to the on-policy objective. Guided by this signal, we further propose f-OPD, a novel framework that adaptively regulates stale-sample influence and constrains policy drift accumulated under asynchronous training. Across reasoning, tool-use, and coding-agent tasks of increasing interaction horizon, f-OPD consistently achieves task performance comparable to synchronous optimization while largely retaining the throughput advantages of asynchronous execution. Our results establish the first recipe for achieving a performance-efficiency trade-off in OPD, paving the way for long-horizon agentic post-training at scale.

Black-box knowledge distillation for large language models presents a strict trade-off. Simple off-policy methods (e.g., sequence-level knowledge distillation) struggle to correct the student's inherent errors. Fully on-policy methods (e.g., Generative Adversarial Distillation) solve this via adversarial training but introduce well-known training instability and crippling computational overhead. To address this dilemma, we propose SODA (Semi On-policy Distillation with Alignment), a highly efficient alternative motivated by the inherent capability gap between frontier teachers and much smaller base models. Because a compact student model's natural, zero-shot responses are almost strictly inferior to the powerful teacher's targets, we can construct a highly effective contrastive signal simply by pairing the teacher's optimal response with a one-time static snapshot of the student's outputs. This demonstrates that exposing the small student to its own static inferior behaviors is sufficient for high-quality distribution alignment, eliminating the need for costly dynamic rollouts and fragile adversarial balancing. Extensive evaluations across four compact Qwen2.5 and Llama-3 models validate this semi on-policy paradigm. SODA matches or outperforms the state-of-the-art methods on 15 out of 16 benchmark results. More importantly, it achieves this superior distillation quality while training 10 times faster, consuming 27% less peak GPU memory, and completely eliminating adversarial instability.

On-policy distillation (OPD) trains a student policy by matching a stronger teacher on the student's own trajectories, offering a promising framework for language agent training. However, its application to long-horizon agentic tasks remains insufficiently explored. We identify two key inefficiencies in vanilla agent OPD: (1) full-horizon rollouts often waste wall-clock resources on tail turns that provide weak and noisy KL supervision, and (2) trajectory-level KL objectives concentrate most of the loss on shallow tokens, leaving deeper decision turns under-trained once initial behaviors are aligned. To address these challenges, we propose TurnOPD, a turn-level budgeting strategy for efficient on-policy distillation of long-horizon agents. TurnOPD consists of two budget controllers: adaptive rollout-depth budgeting, which uses probe-based turn statistics to determine rollout length, and progressive turn-normalized loss budgeting, which gradually shifts KL weighting from token-level to turn-balanced supervision. Experiments on ALFWorld, WebShop, and Multi-Hop Search with task-specialized teacher models show that TurnOPD achieves superior validation accuracy under equal wall-clock training budgets and advances the accuracy--time frontier beyond vanilla OPD.

On-policy distillation (OPD) supervises the student only in output space by matching next-token probabilities. This output-only paradigm has two limits: (1) sampling variance from Monte Carlo KL estimates over large vocabularies (e.g., Qwen's ~150k tokens) persists throughout training, and (2) it treats the teacher as a black-box, discarding all intermediate hidden states after the LM head. We propose On-Policy Representation Distillation (OPRD), which lifts distillation into hidden-state space by aligning student and teacher representations across selected layers on the same rollouts, bypassing the LM head entirely. Theoretically, OPRD eliminates sampling variance and provides richer per-layer structural information. Empirically, OPRD closes the student-teacher gap on AIME 2024/2025 and AIMO, while output-space OPD baselines plateau below the teacher. OPRD also trains 1.44x faster and uses 54% less memory than top-k OPD. Code: https://github.com/ShenzhiYang2000/OPRD.

On-policy distillation (OPD) has emerged as an efficient post-training paradigm for large language models. However, existing studies largely attribute this advantage to denser and more stable supervision, while the parameter-level mechanisms underlying OPD's efficiency remain poorly understood. In this work, we argue that OPD's efficiency stems from a form of ``foresight'': it establishes a stable update trajectory toward the final model early in training. This foresight manifests in two aspects. First, at the Module-Allocation Level, OPD identifies regions with low marginal utility and concentrates updates on modules that are more critical to reasoning. Second, at the Update-Direction Level, OPD exhibits stronger low-rank concentration, with its dominant subspaces aligning closely with the final update subspace early in training. Building on these findings, we propose EffOPD, a plug-and-play acceleration method that speeds up OPD by adaptively selecting an extrapolation step size and moving along the current update direction. EffOPD requires no additional trainable modules or complex hyperparameter tuning, and achieves an average training acceleration of 3times while maintaining comparable final performance. Overall, our findings provide a parameter-dynamics perspective for understanding the efficiency of OPD and offer practical insights for designing more efficient post-training methods for large language models.

On-policy distillation (OPD) trains a student on prefixes sampled from its own policy while matching a stronger teacher. This addresses the prefix mismatch of offline distillation, but early student rollouts can still be poor, placing teacher supervision on weak or low-quality prefixes. We propose Trust-Region behavior Blending (TRB), a warmup method that replaces the early rollout policy with the closest-to-teacher behavior policy inside a student-centered KL trust region, while keeping the per-prefix reverse-KL OPD loss unchanged. The KL budget is annealed to zero, so training returns to pure student rollouts after warmup. Across two math-reasoning distillation settings, TRB attains the strongest average among the compared methods.

On-policy distillation is a promising approach for transferring knowledge between language models, where a student learns from dense token-level signals along its own trajectories. This framework typically uses reverse KL divergence, encouraging the student to match the teacher's high-confidence predictions. However, we show that the mode-seeking property of reverse KL reduces generation diversity and yields unstable learning signals when the teacher distribution has high entropy. To address this, we introduce Entropy-Aware On-Policy Distillation. Our key idea is augmenting the standard reverse KL objective with forward KL when teacher entropy is high, capturing the full range of plausible outputs while retaining precise imitation elsewhere. It balances mode-seeking precision with mode-covering robustness without sacrificing on-policy training efficiency. Experiments show that our method maintains generation diversity (sustained token-level entropy) and improves student-teacher alignment (lower forward KL on high-entropy tokens). Across six math reasoning benchmarks, this yields Pass@8 accuracy gains of +1.37 for Qwen3-0.6B-Base, +2.39 for Qwen3-1.7B-Base, and +5.05 for Qwen3-4B-Base compared to baseline on-policy distillation methods. These results demonstrate that accounting for teacher uncertainty is essential for maintaining diversity and achieving effective knowledge transfer.

On-Policy Self-Distillation (OPSD) has recently emerged as an alternative to Reinforcement Learning with Verifiable Rewards (RLVR), promising higher accuracy and shorter responses through token-level credit assignment from a self-teacher conditioned on privileged context. However, this promise does not carry over to thinking-enabled mathematical reasoning, where reported accuracy gains shrink and sometimes turn negative. We hypothesize that hindsight supervision can specify better token-level alternatives in short thinking-disabled outputs, but in long thinking-enabled traces it more readily identifies redundancy than supplies better replacements. To test this, we applied OPSD separately to correct and incorrect rollout groups, so that compression and correction can be observed in isolation. Our results show that in thinking-enabled mathematical reasoning, OPSD behaves most reliably as a compression mechanism rather than a correction mechanism: training only on correct rollouts preserves accuracy while substantially shortening responses, whereas training only on incorrect rollouts damages accuracy. In light of these findings, we propose a revised post-training pipeline for thinking-enabled mathematical reasoning: SFT then RLVR then OPSD.

Adapting large language models (LLMs) to long-context tasks requires post-training methods that remain accurate and coherent over thousands of tokens. Existing approaches are limited in several ways: 1) off-policy methods such as supervised fine-tuning (SFT) and knowledge distillation (KD) suffer from exposure bias and limited recovery from model-generated errors over long horizons; 2) on-policy reinforcement learning methods such as Group Relative Policy Optimization (GRPO) better align training with model-generated states, but are unstable and sample-inefficient due to sparse rewards; 3) on-policy distillation (OPD) provides dense token-level guidance, but does not directly optimize arbitrary reward signals. In this paper, we propose Distilled Group Relative Policy Optimization (dGRPO), a method for long-context reasoning that augments GRPO with dense guidance from a stronger teacher via OPD. We also introduce LongBlocks, a synthetic long-context dataset spanning multi-hop reasoning, contextual grounding, and long-form generation. We conduct extensive experiments and ablations comparing off-policy training, sparse-reward GRPO, and our combined approach, leading to an improved recipe for long-context alignment. Overall, our results show that combining outcome-based policy optimization with knowledge distillation in a single objective provides a more stable and effective path to long-context reasoning, while preserving short-context capabilities.

Reinforcement learning has emerged as a powerful tool for improving diffusion-based text-to-image models, but existing methods are largely limited to single-task optimization. Extending RL to multiple tasks is challenging: joint optimization suffers from cross-task interference and imbalance, while cascade RL is cumbersome and prone to catastrophic forgetting. We propose DiffusionOPD, a new multi-task training paradigm for diffusion models based on Online Policy Distillation (OPD). DiffusionOPD first trains task-specific teachers independently, then distills their capabilities into a unified student along the student own rollout trajectories. This decouples single-task exploration from multi-task integration and avoids the optimization burden of solving all tasks jointly from scratch. Theoretically, we lift the OPD framework from discrete tokens to continuous-state Markov processes, deriving a closed-form per-step KL objective that unifies both stochastic SDE and deterministic ODE refinement via mean-matching. We formally and empirically demonstrate that this analytic gradient provides lower variance and better generality compared to conventional PPO-style policy gradients. Extensive experiments show that DiffusionOPD consistently surpasses both multi-reward RL and cascade RL baselines in training efficiency and final performance, while achieving state-of-the-art results on all evaluated benchmarks.

Long-horizon tool-use reinforcement learning learns from outcome verification, but trajectory-level advantages are broadcast over reasoning, API, and answer tokens. Direct self-distillation can supply a denser signal, but in our experiments it can also destroy tool use by rehearsing teacher behavior without identifying which actions the verifier rewards. We introduce Sibling-Guided Credit Distillation (SGCD), which uses distillation for bounded credit weighting rather than as a competing actor loss. Dynamic sampling produces mixed successful and failed sibling rollouts; an external LLM summarizes their contrast into a training-only credit reference; and detached teacher/student divergence reshapes GRPO token advantages. The deployed student receives only the clean task prompt. Across AppWorld and tau^3-airline, SGCD reports higher held-out point estimates than GRPO-family comparators: AppWorld TGC improves from 42.9 to 45.6 on test_normal and from 24.7 to 27.0 on test_challenge, and tau^3-airline held-out evaluator score improves from 0.583 to 0.602. These results support a narrow design rule for long-horizon tool-use agents: use distillation to guide credit assignment while keeping policy gradient in charge of the actor update.

On-policy distillation (OPD) has become a key paradigm in LLM post-training, yet its training dynamics remain poorly understood. We present a systematic study examining the role, pathologies, and regulations of OPD. We first clarify the role of OPD as an exploration catalyst: it steers the student toward correct reasoning paths via dense token-level guidance, without expanding capability ceiling. We confirm this by showing that prompt diversity matters more than per-problem sampling numbers, and critically, that the effectiveness of OPD hinges entirely on the quality of its guiding signal. This dependency exposes two pathologies that derail exploration. The Student-Teacher Mismatch occurs when a large teacher-student distributional gap causes the guiding signal to misalign with task correctness, steering exploration in counterproductive directions. Length Exploitation arises when the aggregated token-level objective creates length-dependent shortcuts, allowing the student to game the reward landscape through response truncation or redundant padding, exploring degenerate length modes rather than reasoning strategies. To tame these pathologies, we investigate lightweight signal regulations: advantage clipping and log-scale compression, ensuring exploration is guided by faithful signals. Experiments across seven benchmarks demonstrate that these regulations alleviate length exploitation and enable effective distillation, stably surpassing OPD variants and RLVR baselines, thereby confirming that well-regulated signal quality, rather than mere teacher scale, governs successful exploration in OPD.

Agentic search enables large language models to solve knowledge-intensive tasks by interleaving multi-step reasoning with retrieval, yet optimizing this with outcome-based reinforcement learning (RL) provides only sparse supervision. Knowledge distillation can supply denser guidance, and advanced proprietary models with their strong reasoning capabilities are promising teachers. While distilling from proprietary models can densify this supervisory signal, conventional logit-matching is precluded by hidden logits and mismatched tokenizers, whereas raw natural language trajectory imitation transfers superficial stylistic artifacts rather than core reasoning competence. To address the heterogeneous distillation problem and bridge the distribution gap, we propose Multi-Agent Protocol Distillation (MAPD), a joint distillation and RL framework uses a structured, style-normalized protocol as an intermediate representation. An offline multi-agent system (MAS) decomposes each query, retrieves supporting evidence, repairs failed searches, and converts the resulting exploration trace into a JSON protocol containing the task type, reasoning plan, and extractive grounding facts. During training, the protocol is provided only to a privileged branch of the student policy, whose token distributions furnish a dense distillation signal alongside the sparse RL objective. Extensive evaluations across seven QA benchmarks demonstrate that MAPD consistently outperforms competitive distillation and RL, achieving average success rates of 39.4\% on Qwen3-1.7B and 44.4\% on Qwen3-4B. Crucially, the framework generalizes robustly across diverse proprietary teachers while effectively mitigating the student policy from style drift and verbosity degeneration.

On-policy distillation (OPD), which aligns a student with the teacher's token-level distribution on the student's own rollouts, is an effective paradigm for transferring capabilities across LLMs. Prevailing approaches assume a teacher at least as capable as the student: they either distill a larger model into a smaller one, which fails at the frontier where no larger teacher exists, or consolidate multiple domain experts trained from a shared base, which requires costly training at the student's scale. We introduce Weak-to-Strong On-Policy Distillation (W2S-OPD), a simple yet effective OPD framework that improves the strong student by distilling from multiple weak models. W2S-OPD constructs a proxy teacher in logit space from a contrast pair of a positive and a negative model, both smaller than the student and cheap to obtain. Their logit difference isolates the capability direction, which is added to the student's own base model, yielding a proxy teacher that couples this direction while staying distributionally adjacent to the student. The student then distills it by minimizing the per-token reverse KL on its own rollouts. We instantiate the contrast pair as i) a post-RL expert against its pre-RL initialization, isolating the skill RL instills, ii) a larger against a smaller base model, isolating the capability from scale, and iii) a small base model with correct versus wrong hints, isolating the instance-level direction toward the solution. Across four math and three code benchmarks, W2S-OPD outperforms OPD, enables the student to surpass the domain teacher, and keeps improving the student even when every supervision source is weaker. Analysis shows different contrasts yield distinct signals: the post-RL and hint contrasts emphasize reasoning frameworks, while the scale contrast emphasizes the solving procedure. Our code will be available at https://github.com/Yu-Fangxu/W2S-OPD.

On-policy distillation (OPD) trains a student on its own rollouts guided by teacher feedback and is becoming increasingly important for large language model (LLM) post-training. Like reinforcement learning (RL), however, OPD faces an on-policy systems bottleneck, as rollouts can dominate training time for reasoning workloads. Asynchronous training pipelines can alleviate this bottleneck by decoupling rollout generation from learner updates, but doing so introduces stale-policy data. While prior work has studied stale data in asynchronous RL, its effects in OPD remain underexplored. We present the first systematic study of staleness in asynchronous OPD, focusing on a practical setting where teacher feedback is implemented through local KL losses and full-vocabulary teacher logits are too expensive to store or transfer, necessitating finite teacher-score caches. We first show that KL direction changes the stale-data problem: teacher-weighted forward KL is more robust to stale rollouts, whereas student-weighted reverse KL is vulnerable. Second, for this vulnerable reverse-KL case, we study whether methods designed to stabilize asynchronous RL can mitigate OPD staleness. In our experiments, they do not improve over a simpler OPD-specific surrogate: recomputing the reverse-KL signal under the current student at learner time. Third, we analyze how finite teacher-score caches create a bias-variance tradeoff for sparse and sampled reverse-KL OPD estimators. This motivates multi-sample Monte Carlo (MC), which preserves MC correctability while reducing one-sample variance. Finally, we present and open-source AsyncOPD, a fully asynchronous OPD training pipeline built from these estimator choices. Experiments show that AsyncOPD improves training throughput by 1.6times to 3.8times over strict synchronous training while reaching comparable accuracy.

Diffusion distillation models effectively accelerate reverse sampling by compressing the process into fewer steps. However, these models still exhibit a performance gap compared to their pre-trained diffusion model counterparts, exacerbated by distribution shifts and accumulated errors during multi-step sampling. To address this, we introduce Distillation++, a novel inference-time distillation framework that reduces this gap by incorporating teacher-guided refinement during sampling. Inspired by recent advances in conditional sampling, our approach recasts student model sampling as a proximal optimization problem with a score distillation sampling loss (SDS). To this end, we integrate distillation optimization during reverse sampling, which can be viewed as teacher guidance that drives student sampling trajectory towards the clean manifold using pre-trained diffusion models. Thus, Distillation++ improves the denoising process in real-time without additional source data or fine-tuning. Distillation++ demonstrates substantial improvements over state-of-the-art distillation baselines, particularly in early sampling stages, positioning itself as a robust guided sampling process crafted for diffusion distillation models. Code: https://github.com/geonyeong-park/inference_distillation.

Diffusion large language models (DLLMs) have the potential to enable fast text generation by decoding multiple tokens in parallel. However, in practice, their inference efficiency is constrained by the need for many refinement steps, while aggressively reducing the number of steps leads to a substantial degradation in generation quality. To alleviate this, we propose a trajectory self-distillation framework that improves few-step decoding by distilling the model's own generative trajectories. We incorporate Direct Discriminative Optimization (DDO), a reverse-KL objective that promotes mode-seeking distillation and encourages the student to concentrate on high-probability teacher modes. Across benchmarks, our approach consistently outperforms strong few-step baselines and standard training under tight step budgets. Although full-step decoding remains superior, we substantially narrow the gap, establishing a strong foundation towards practical few-step DLLMs. The source code is available at https://github.com/Tyrion58/T3D.

Standard LLM distillation wastes compute on two fronts: problems the student has already mastered (near-zero gradients) and problems far beyond its reach (incoherent gradients that erode existing capabilities). We show that this waste is not merely intuitive but structurally inevitable: the gradient signal-to-noise ratio in distillation provably vanishes at both pass-rate extremes. This theoretical observation leads to Paced, a framework that concentrates distillation on the zone of proximal development -- the frontier of a student model's competence -- via a principled pass-rate weight w(p) = p^α(1 - p)^β derived from the boundary-vanishing structure of distillation gradients. Key results: (1) Theory: We prove that the Beta kernel w(p) = p^α(1-p)^β is a leading-order weight family arising from the SNR structure of distillation, and that it is minimax-robust -- under bounded multiplicative misspecification, worst-case efficiency loss is only O(δ^2). (2)Distillation: On distillation from a larger teacher to a smaller student model with forward KL, Paced achieves significant gain over the base model, while keeping benchmark forgetting at a low level. (3)Self-distillation: On instruction-tuned models with reverse KL, gains are exceeding baselines as well. (4)Two-stage synergy: A forward-KL-then-reverse-KL schedule yields the strongest results in our setting, reaching substantial improvements on standard reasoning benchmarks -- supporting a mode-coverage-then-consolidation interpretation of the distillation process. All configurations require only student rollouts to estimate pass rates, need no architectural changes, and are compatible with any KL direction.

On-policy distillation (OPD) adapts diffusion models by querying a teacher along trajectories generated by the current student, but how it should behave under classifier-free guidance (CFG), a default component of modern diffusion systems, remains poorly understood. Existing OPD methods naturally extend velocity matching to the CFG-composed prediction, directly matching teacher and student guided velocities. We show that this objective is under-identified at the branch level: positive- and negative-branch errors can compensate in the guided prediction. Through two contrasting cases, we find that naive matching remains effective under shared negative conditioning, where both branch errors decrease jointly. When the model's native CFG schema retains privileged information in the teacher's negative branch that is unavailable to the student, however, this joint reduction breaks down and the composed objective induces antagonistic branch-error dynamics, reducing the positive-branch error while increasing the negative-branch error. We term this failure mode Negative Branch Asymmetry (NBA). To address NBA, we introduce Positive--Direction Matching (PDM), a branch-aware OPD objective that separately constrains the positive prediction and the CFG conditional direction. We apply PDM to dense-to-sparse video control, where naive guided matching is highly sensitive to inference guidance scales, while branch-aware supervision enables more robust and effective knowledge transfer.

On-policy distillation (OPD) has become a core technique in the post-training of large language models, yet its training dynamics remain poorly understood. This paper provides a systematic investigation of OPD dynamics and mechanisms. We first identify that two conditions govern whether OPD succeeds or fails: (i) the student and teacher should share compatible thinking patterns; and (ii) even with consistent thinking patterns and higher scores, the teacher must offer genuinely new capabilities beyond what the student has seen during training. We validate these findings through weak-to-strong reverse distillation, showing that same-family 1.5B and 7B teachers are distributionally indistinguishable from the student's perspective. Probing into the token-level mechanism, we show that successful OPD is characterized by progressive alignment on high-probability tokens at student-visited states, a small shared token set that concentrates most of the probability mass (97%-99%). We further propose two practical strategies to recover failing OPD: off-policy cold start and teacher-aligned prompt selection. Finally, we show that OPD's apparent free lunch of dense token-level reward comes at a cost, raising the question of whether OPD can scale to long-horizon distillation.

Large language model (LLM) post-training is essential for improving reasoning, adaptation, and alignment. Existing methods mainly follow two paradigms: reinforcement learning (RL) and on-policy distillation (OPD). However, RL relies on coarse-grained outcome supervision, resulting in difficult credit assignment and limited capability to acquire new knowledge. OPD, meanwhile, unconditionally matches teacher logits through KL divergence, which creates a dilemma: similar teachers provide little new knowledge, while substantially different teachers often yield ineffective guidance, largely restricting OPD to within-family distillation. We propose Distilled Reinforcement Learning (Distilled RL), which integrates teacher supervision into the RL objective to provide fine-grained guidance, selectively transfer new knowledge and avoid unconditional imitation. Distilled RL contains three components: reverse importance sampling with clipping, negative sample reset, and sequence-level geometric normalization. Through a concise and interpretable case study, we demonstrate that Distilled RL can effectively transfer previously unavailable knowledge from a teacher model to a student model. Extensive experiments across both within-family and cross-family distillation settings show that Distilled RL substantially outperforms standard RL and OPD in terms of both pass@1 and pass@k. Our code is available at https://github.com/597358816/Distilled-RL.

On-policy self-distillation (OPSD) trains a model on its own rollouts and uses a frozen copy to provide dense token-level targets conditioned on a reference target. This works well for LLM reasoning, but a direct extension to multimodal large language models (MLLMs) can create a shortcut: the privileged target may guide tokens mainly based on the text reference target rather than the image. We propose ViGOS, a visually grounded OPSD framework for MLLM post-training. The student first writes a visual description and then reasons toward the final answer. For valid rollouts, an image-only perception teacher supervises the description, while a privileged reasoning teacher supervises the reasoning and final answer on the same student prefix. A reference teacher is used only for invalid rollouts to recover the output format. Across general vision-language, expert reasoning, visual math, spatial grounding, and visual-language-prior benchmarks, ViGOS keeps the main benefits of OPSD and improves image-grounded behavior in shortcut-prone settings.

On-policy distillation (OPD) has emerged as an efficient post-training paradigm for large language models. However, standard OPD requires a live teacher inference server throughout training, resulting in substantial infrastructure overhead. In this work, we investigate whether on-policy distillation can be performed offline. A natural approach is to precompute teacher log-probabilities once over SFT rollouts and reuse them during training. In practice, however, this offline variant fails to reliably match the performance of standard OPD. To understand this discrepancy, we identify a previously overlooked condition that is critical for any OPD pipeline, which we term teacher consistency. This condition requires that the same teacher model be used for both supervised fine-tuning and OPD. We show that violating teacher consistency introduces an irreducible gradient bias, causing both offline and online OPD to converge to a suboptimal fixed point regardless of training duration. Building on this insight, we propose Lightning OPD, an offline on-policy distillation framework that enforces teacher consistency by precomputing teacher log-probabilities over SFT rollouts. This design eliminates the need for a live teacher server entirely. We further show that, under teacher consistency, Lightning OPD shares the same optimum as standard OPD, with bounded gradient discrepancy and an implicit regularization effect that helps prevent policy drift. Extensive experiments on mathematical reasoning and code generation demonstrate that Lightning OPD achieves state-of-the-art performance with significantly improved efficiency. Starting from an SFT-initialized Qwen3-8B-Base model, Lightning OPD reaches 69.9% on AIME 2024 in just 30 GPU hours, achieving a 4.0x speedup over standard OPD and substantially lowering the barrier to entry for academic research on LLM post-training.

Big goals are hard to achieve all at once; breaking them into small steps is wiser. We present Trust Region Policy Distillation (TOP-D), which transforms the notoriously unstable, high-variance On-Policy Distillation (OPD) into a stable training paradigm by dynamically constructing a proximal teacher. Theoretically, we establish a rigorous framework demonstrating that TOP-D inherently controls gradient variance. By providing a formal global convergence analysis alongside a monotonic improvement bound, we mathematically formalize the reliability and stability of the overall training dynamics. Empirically, TOP-D dramatically enhances training stability, sample efficiency, and final performance on mathematical reasoning tasks. More importantly, TOP-D introduces zero additional computational overhead, positioning itself as a promising alternative to the well-established OPD paradigm.

Distilling large language models (LLMs) typically involves transferring the teacher model's responses through supervised fine-tuning (SFT). However, this approach neglects the potential to distill both data (output content) and reward signals (quality evaluations). Extracting reliable reward signals directly from teacher models is challenging, as LLMs are optimized for generation rather than evaluation, often resulting in biased or inconsistent assessments. To address this limitation, we propose a novel distillation pipeline that transfers both responses and rewards. Our method generates pseudo-rewards through a self-supervised mechanism that leverages the inherent structure of both teacher and student responses, enabling reward learning without explicit external evaluation. The reward model subsequently guides reinforcement learning (RL), allowing iterative refinement of the student model after an SFT warm-up phase. Experiments on GSM8K and MMLU-PRO demonstrate that our method consistently outperforms traditional SFT-based approaches, enabling student models to surpass the performance of their teachers. This work highlights the potential for scalable, efficient distillation through structured self-supervised reward learning, reducing dependence on external reward supervision.

On-policy distillation (OPD), which supervises a student on its own sampled trajectories, has emerged as a data-efficient post-training method for improving reasoning while avoiding the reward dependence of reinforcement learning and the catastrophic forgetting often observed in standard supervised fine-tuning. However, standard OPD typically computes teacher supervision under noisy student-generated contexts and often relies on a single stochastic teacher rollout per prompt. As a result, the supervision signal can be high-variance: the sampled teacher trajectory can be incorrect, uninformative, or poorly matched to the student's current reasoning behavior. To address this limitation, we propose BRTS, a Best-of-N Rollout Teacher Selection framework for on-policy distillation. BRTS augments standard student-context OPD with a teacher-context supervision branch constructed from the curated teacher trajectory. Rather than distilling from the first sampled teacher rollout, BRTS samples a small pool of teacher trajectories and selects the auxiliary trajectory using a simple priority rule: correctness first, student alignment second. When multiple correct teacher trajectories are available, BRTS chooses the one most aligned with the student's current behavior; when unconditioned teacher samples fail on harder prompts, it invokes a ground-truth-conditioned recovery step to elicit a natural derivation. The selected trajectory is then used to provide reliable teacher-context supervision inside the OPD loop, augmented with an auxiliary loss on the teacher trajectory. Experiments on AIME 2024, AIME 2025, and AMC 2023 show that BRTS improves over standard OPD on challenging reasoning benchmarks, with the largest gains on harder datasets. Our code is available at https://github.com/BWGZK-keke/BRTS.

Reinforcement learning (RL) has emerged as a promising paradigm for inducing explicit reasoning behaviors in large language and vision-language models. However, reasoning-oriented RL post-training remains fundamentally challenging due to sparse trajectory-level rewards, leading to ambiguous credit assignment and severe exploration failures that can trap the policy in a ``learning cliff.'' Recent on-policy distillation methods introduce dense teacher supervision to stabilize optimization, but apply it uniformly across all generated trajectories. We argue that such uniform distillation is ill-suited for reasoning-intensive tasks, as low-quality on-policy trajectories often originate from early logical errors, and distillation under flawed contexts injects noisy and misaligned gradients. To address these challenges, we propose Knowledge-Enhanced Preference Optimization (KEPO), a unified post-training framework that integrates: (i) a quality-gated on-policy distillation objective that selectively applies dense teacher guidance only to high-quality trajectories, and (ii) a knowledge-enhanced exploration strategy that leverages hints learned from a teacher model to rejectively sample reward-positive on-policy trajectories for RL, thereby mitigating exploration collapse. Evaluated on a challenging medical visual question answering benchmark under single-source generalization, KEPO demonstrates improved training stability, more coherent reasoning behaviors, and superior out-of-distribution performance over reinforcement learning and on-policy distillation baselines.

Majorities of distillation methods on pre-trained diffusion models or on pre-trained rectified flow, focus on either the distillation outputs or the trajectories between random noises and clean images to speed up sample generations from pre-trained models. In those trajectory-based distillation methods, consistency distillation requires the self-consistent trajectory projection to regulate the trajectory, which might avoid the common ODE approximation error {while still be concerning about sampling efficiencies}. At the same time, rectified flow distillations enforce straight trajectory for fast sampling, although an ODE solver is still required. In this work, we propose a trajectory distillation method, \modelname, that enjoys the benefits of both and enables few-step generations. TraFlow adopts the settings of consistency trajectory models, and further enforces the properties of self-consistency and straightness throughout the entire trajectory. These two properties are pursued by reaching a balance with following three targets: (1) reconstruct the output from pre-trained models; (2) learn the amount of changes by pre-trained models; (3) satisfy the self-consistency over its trajectory. Extensive experimental results have shown the effectiveness of our proposed method.