On-Policy Distillation

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Overview

On-policy distillation studies how to transfer a teacher’s capabilities by training a student on trajectories the student generates, rather than only on fixed teacher-written examples. Common approaches match teacher and student token distributions with KL-style objectives, often combining this dense feedback with verifier rewards, reinforcement learning, or feedback from successful peer attempts. Work spans language-model reasoning and tool-using agents as well as multimodal, speech, diffusion, and embodied models; methods increasingly select useful tokens, turns, or rollout lengths to reduce compute. A central tension is that student-generated states can make supervision more relevant, but teacher signals may be unreliable or mismatched, and repeated rollouts can be costly or destabilize training. 4 sentences total.

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511 papers178 papers in the last four weeks, up 141% on the four weeks before. 1.0% of all new papers.

Sep 7, 2026

Flow3D-OPD: Multi-Teacher On-Policy Distillation for 3D Geometry Generation with Flow-Matching Diffusion Transformer

Recent image-to-3D generation models built on flow-matching diffusion Transformers (DiT) can produce high-fidelity meshes, yet their post-training strategy remains largely unexplored. There exist several critical bottlenecks in reinforcement learning: the inherent difficulty of defining comprehensive rewards for 3D geometric quality, and the gradient interference that arises when jointly optimizing heterogeneous objectives. Inspired by the practicability of on-policy distillation (OPD) in large language models and image generation, we propose Flow3D-OPD, a two-stage post-training framework that introduces multi-teacher distillation into 3D geometry generation. In the first stage, we utilize the semi-policy to enhance the foundational capability of the pretrained model and then design an agentic verifier for 3D geometric quality evaluation. Based on the verifier, we could cultivate domain-specialized teacher models via direct preference optimization (DPO). In the second stage, we consolidate heterogeneous expertise into a unified student model through on-policy distillation with hard task-routing sampling and gradient accumulation, which could mitigate the gradient interference in joint optimization. Without relying on elaborate modifications, our straightforward yet effective design achieves consistent improvements across all geometric quality dimensions and surpasses all teacher models in the average metric. Extensive experiments demonstrate that our approach provides an effective paradigm for reinforcement learning in 3D generation.

Zhiwei Ning, Zhen Zhou, Puhua Jiang +7

Shanghai Jiao Tong University · Tencent Hunyuan3D · Zhejiang Normal University +1

3D Mesh GenerationDiffusion Model DistillationRL for Generative ModelsOn-Policy Distillation3D Diffusion Models
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Sep 6, 2026

Teacher Should Think Ahead: Adaptive Continuations for Reliable On-Policy Distillation

On-policy distillation (OPD) is a promising approach for transferring knowledge between language models, where a student receives dense token-level supervision along its own generated trajectories. However, teacher supervision can be unreliable when conditioned on incomplete or low-quality student prefixes. We identify Teacher Uncertainty Contraction (TUC), a systematic phenomenon whereby the teacher's predictive uncertainty decreases as it continues from a student-generated prefix. We theoretically characterize this trade-off through a variance-bias decomposition of teacher-branch gradients, showing that uncertainty contraction reduces variance while teacher-student path divergence increases bias, thereby favoring a finite continuation. Guided by this insight, we propose Adaptive-Continuations On-Policy Distillation (AC-OPD), which augments informative states along student rollouts with teacher continuations and adaptively selects their effective supervision horizons. Experiments on mathematical reasoning and code generation across model scales demonstrate that AC-OPD consistently improves over standard OPD. Controlled-continuations and matched-budget analyses further validate the adaptive-continuations design, highlighting adaptive teacher continuations as an effective principle for reliable on-policy distillation.The code will be made publicly available upon publication.

Jingang Zhou, Yuyi Zhou, Haiyang Guo +6

School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences · Institute of Automation, Chinese Academy of Science · Ant Group

Language Model DistillationOn-Policy DistillationTeacher-Student LearningUncertainty-Aware Knowledge Distillation
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Sep 6, 2026

Teaching a Moving Student: Rethinking the Curriculum of On-Policy Distillation

In on-policy distillation (OPD), the student determines which states receive teacher supervision. As its policy evolves, earlier response prefixes become less likely even though teacher-student disagreement on them persists. Under matched trajectory and optimization budgets, neither more queries nor more frequent rollout resampling is uniformly beneficial. Current-policy rollouts outperform initial-policy rollouts at shorter response budgets, but this ranking reverses at longer budgets. Replaying initial-policy rollouts after current-policy training improves accuracy, whereas replaying fixed recent rollouts does not reproduce the gain. We propose R-OPD, a gradient-triggered curriculum that adaptively selects when to revisit initial-student trajectories. When changes in mean gradients fall within minibatch-level variation for two consecutive comparisons, training switches from the next iteration onward to initial-policy replay. Across eight mathematics benchmarks and three training-data orders, R-OPD improves average accuracy over continued current-policy sampling by 2.25/4.44 percentage points at 16K/32K for a 0.6B student and 2.81/6.15 points for a 1.7B student. With a 30B-A3B teacher, it improves 8B accuracy by 4.05 points at 32K. At 32K, R-OPD exceeds a fixed schedule of 40 current-policy updates followed by 20 replay updates by 1.39/1.66/1.85 points for 0.6B/1.7B/8B. At the same generation cap, R-OPD also produces longer responses, suggesting that well-timed revisits help students use more of their reasoning capacity.

Lingxiang Hu, Tianle Xia, Yiding Sun +6

Tencent

Language Model DistillationOn-Policy DistillationCurriculum Learning
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Sep 4, 2026

RISE: Recursive Improvement via Self-Extrapolating Policy Distillation

On-policy distillation (OPD) provides dense, per-token supervision for language model post-training, but its effectiveness is bottlenecked by teacher quality: external teachers suffer from distribution mismatch, while self-distillation with privileged conditioning is limited by in-context learning capacity. We propose RISE (Recursive Improvement via Self-Extrapolating Policy Distillation), which constructs a synthetic teacher directly from the model's own RLVR training trajectory. By extrapolating the displacement between the current checkpoint and a trailing anchor---in parameter space or output logit space---RISE converts a sparse outcome-induced parameter update into a dense token-level target, without any external model or privileged conditioning. RISE combines RLVR and OPD in a complementary loop: outcome rewards ground the extrapolation toward correct reasoning, while the extrapolated teacher refines token-level decisions. Moreover, since the teacher is refreshed every iteration as the student improves, distillation becomes a recursive improvement mechanism rather than a one-shot compression step. Experiments spanning mathematical reasoning, multi-domain STEM, code generation, and multi-turn agentic tasks show that RISE outperforms RLVR-only training and on-policy self-distillation across all settings.

Yang Li, Semih Yavuz, Shafiq Joty

Salesforce AI Research

Language Model DistillationOn-Policy DistillationRL for Language Model Reasoning
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Sep 4, 2026

What Matters in On-Policy Distillation? A Perspective on Data Efficiency and Data Selection

On-Policy Distillation (OPD) has emerged as a widely adopted post-training paradigm for enhancing large language models in reasoning domains. However, the data-centric mechanisms in OPD remain relatively underexplored. This paper presents an empirical study of data efficiency and data selection in OPD. We begin by investigating an extreme setting: training OPD on only one example, namely 1-shot OPD. Surprisingly, we find that 1-shot OPD is consistently effective across all sampled training examples and harder examples often yield superior performance gain. We next investigate what actually drives the student model's improvement in the training data. Our analysis reveals that the improvement is not driven by high token entropy, but the longer CoT paths which hard problem naturally generate. Training on longer CoT can help maintain closer alignment with the teacher over a long reasoning horizon, and learn critical thinking patterns usually missing in short CoTs, such as reflection (e.g., "Alternatively"). Based on these insights, we propose a simple data selection method that selects only hard examples for training, where even "unsolvable" examples that completely exceed the teacher's capability can be successfully used. Our experiments conducted on five models ranging from 1.5B to 8B show that training the student model on only 8 selected hard examples matches the performance of the 17K dataset baseline. Code and models will be publicly available.

Zhinan Hou, Jiaqi Zhang, Xunliang Cai +1

Tsinghua University · Meituan LongCat Team

Language Model DistillationOn-Policy DistillationKnowledge DistillationCoT Reasoning
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Sep 4, 2026

Persistent Teacher Anchoring for Tool-Using Agents

Distillation is common in LLM post-training, where on-policy knowledge distillation (OPKD) uses student-generated trajectories to prepare the student for downstream RL. At each state, the student matches a next-token distribution supplied by the teacher. As the rollout enters states the teacher would not visit, the teacher-student distribution gap can accumulate. In tool use, this gap becomes consequential because student-written calls execute before supervision and their observations shape later prefixes. Proposer-verifier generation addresses this drift by letting the teacher decide which student-proposed text is retained during generation. Existing formulations govern text but leave tool execution outside their scope. We propose Persistent Teacher Anchoring (PTA), a student-induced but teacher-committed rollout construction. PTA retains chunk-level verification and adds turn-level commitment, allowing a call to reach the environment only after the teacher has verified the entire turn. Treating verified chunks as atomic generation units, we introduce persistent lookahead, which fills idle rollout capacity by advancing future samples and carrying unfinished ones across student updates under the fixed verifier. Across Search-R1-style retrieval and DeepEyes-style perception RL, applying PTA before downstream RL improves macro best@4 by 2.5 and 2.8 points over OPKD under the same downstream RL budget, while lookahead improves throughput by 24%.

Hyun Bin Park, Kyungho Song, Sangmin Lee +1

Sogang University · University of Michigan, Ann Arbor

LLM Agent TrainingOn-Policy DistillationRL Post-TrainingRL for Tool Use
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Sep 3, 2026

Extremely Sparse Supervision Incentivizes Reasoning Ability

Large language models demonstrate increasingly strong reasoning capabilities through effective post-training. Yet, prevailing post-training methods optimize over massive numbers of tokens, implicitly assuming that effective learning must be token-intensive. We revisit this assumption in the on-policy distillation (OPD) setting, which naturally admits dense teacher supervision at every generated token. Using the Qwen3 family, we discover a counter-intuitive phenomenon: reasoning can be effectively incentivized by an extremely small fraction of generated tokens--as few as one or two tokens per reasoning trajectory, corresponding to only 0.05% of all tokens. Surprisingly, this sparse supervision in most cases matches or surpasses full-token training in improving reasoning ability, despite excluding the vast majority of generated tokens from the training objective. This phenomenon is consistently observed across nine teacher--student configurations spanning different model scales on mathematical reasoning tasks, and is further validated on coding reasoning, Llama models and Proximal Policy Optimization (PPO)-based reinforcement learning with verifiable reward (RLVR). Interestingly, such extremely sparse supervision may be closer to the natural learning process: rather than correcting every step word by word, one reflects on a few critical reasoning steps, updates prior understanding, and continues the trial-and-error, avoiding micro-level corrections while remaining remarkably effective. Overall, our results challenge the assumption that effective post-training must be token-intensive and point to a new direction for understanding and designing more efficient post-training algorithms.

Zhishuai Liu, Xingzi Xu, Mehmet Saygin Seyfioglu +2

Amazon, Seattle, WA 98109, USA · Duke University, Durham, NC 27708, USA

On-Policy DistillationLanguage Model Post-TrainingLLM Reasoning
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Sep 3, 2026

Rethinking On-Policy Distillation of Large Language Models II: One Training Example

On-policy distillation (OPD) combines student-generated rollouts with dense token-level supervision from a teacher. Existing work has mainly studied its algorithmic behavior, leaving the role of training data unclear. We examine this role at the data-minimal limit by training on a single query. One-shot OPD keeps improving for hundreds of steps and recovers most of full-data OPD's gain across task domains and model families. We explain this result through the states visited during training and the rate at which the student aligns with the teacher. We measure state coverage, the fraction of the states full-data OPD visits that a query set's rollouts reach. A single query already reaches 71.5%71.5\%, most of it within the first 100 steps. Adding semantically distinct queries raises coverage and validation accuracy together, until 16 queries reach 98.9%98.9\% and match full-data training. Yet alignment slows at a similar pace whether OPD trains on one query or the whole dataset, and even a fixed set of states takes hundreds of steps to absorb. OPD is therefore data-overfed but algorithm-starved. Its rollouts quickly expose broad supervision, while the student absorbs that supervision increasingly slowly. The state-coverage result extends to multi-teacher OPD, where 16 semantically diverse queries per domain match full-data MOPD. As a further stress test, content-light templates and off-domain WildChat queries also approach the real-query baseline. Task content and induced state coverage can therefore come apart. We hope these findings direct future work toward the step efficiency of OPD, and prompt a re-examination of the data and the mechanisms behind its recent successes in frontier post-training.

Zixuan Fu, Bingxiang He, Yuxin Zuo +10

Tsinghua University · University of Chinese Academy of Sciences · Northeastern University +2

Language Model DistillationOn-Policy Distillation
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Sep 3, 2026

Sequential Beats Joint: On the Interplay between On-Policy Distillation and RLVR

Reinforcement learning with verifiable rewards (RLVR) and on-policy distillation (OPD) have emerged as two dominant methods for post-training reasoning LLMs. Prior work uses OPD's dense token-level supervision to complement the sparse RL reward, fusing the two signals within a single step: either as a weighted-additive combination or a teacher-modulated rescaling of the RL advantage. In this paper, we show that a simple two-stage scheme, OPD-then-RL, consistently outperforms pure OPD, pure RLVR, and all such joint baselines across logic and math reasoning benchmarks. Beyond the empirical results, we further provide a systematic understanding of this through pass@kk behavior, learning dynamics, and parameter updates, yielding a consistent explanation: OPD expands the student's coverage of teacher-supported solutions and RL sharpens within that support, while jointly optimizing the two signals causes them to interfere. To provide a practical recipe, we find that the OPD validation score is the key signal for when to switch to RL, and that OPD is a better cold start for RL than SFT. Together, our results establish OPD-then-RL as a simple yet strong way to combine the two methods, turning two entangled signals into complementary stages.

Boyan Li, Bingsen Chen, Chenghao Yang +3

University of Alberta · New York University · NYU Shanghai +3

RL for Language Model ReasoningReinforcement Learning with Verifiable RewardsOn-Policy DistillationRL Post-Training
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Sep 2, 2026

Verify Before You Distill: Prompt-Level Teacher Gating for On-Policy Distillation

On-policy distillation (OPD) accelerates post-training by providing dense token-level supervision from a frozen teacher on the student's own rollouts. Vanilla OPD applies this supervision uniformly across prompts, without checking whether the teacher is reliable for each prompt. Because reverse KL is mode-seeking, a confidently wrong teacher can induce a strong yet misleading update. Distributional proxies, such as entropy or teacher-student likelihood agreement, measure uncertainty or agreement but do not directly verify outcome correctness. We introduce Teacher-Gated On-Policy Distillation (TGOPD), built on the principle that teacher reliability should be verified at the prompt level before dense supervision is admitted. TGOPD estimates reliability from a small set of verifier-scored teacher probes and routes each prompt exclusively to dense OPD when the reliability check passes or to verifier-grounded GRPO otherwise. Across 4B and 35B students in mathematics, code, and instruction following, TGOPD outperforms Vanilla OPD in all six single-domain settings and achieves higher seven-benchmark averages at both scales under multi-domain training. By using otherwise-idle teacher capacity for reliability estimation, TGOPD also reduces teacher-side compute waste in asynchronous OPD, increasing teacher-node GPU utilization from 9.8% to 78.9% in the measured 4B single-domain run.

Zhiwei Zhang, Zechen Sun, Fei Zhao +6

AllSpark Team

On-Policy DistillationRL Post-Training
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Sep 2, 2026

Learn from Whoever Is Right: Answer-Verified Multi-Teacher Distillation for Multi-Domain LLMs

Modern large language models (LLMs) rely on reinforcement learning to build strong capabilities in individual domains, but integrating those capabilities into a single deployable model remains challenging. By routing each sample to the teacher whose domain matches it, existing approaches let a domain label decide which teacher provides supervision. However, domain expertise holds only on average: the matched teacher is not always correct on a given sample, while a teacher from another domain sometimes is. The reliable teacher therefore has to be identified per sample, not per domain. In this paper, we introduce Multi-Teacher Self-Distillation Policy Optimization (MT-SDPO), an on-policy distillation method that unifies several frozen teachers into one student model. MT-SDPO consists of three components: (1) self-anchors, where a rollout is supervised by a correct rollout from its own group; (2) answer-verified eligibility, where a teacher may supervise a sample only if its own answer passes a verifier; and (3) privileged distillation, which merges the anchor and all verified feedback into one context that an exponential moving average self-teacher reads and the student does not, thereby keeping one policy at deployment. Across five students from three model families, MT-SDPO lifts the weakest domain of Qwen3-8B by 14.79 points and narrows its domain gap by 74.7%, a better balance than serving one matched teacher per domain. Verified reliability, not domain membership, should decide who teaches. Code is available at https://github.com/hexixiang/MT-SDPO.

Xixiang He, Xingming Li, Baiqi Wu +4

National University of Defense Technology · Zhejiang University · Intelligent Game and Decision Lab

Multi-Teacher Knowledge DistillationSelf-DistillationOn-Policy Distillation
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Sep 2, 2026

CA-OPD: Confidence-Aware On-Policy Distillation for Structured Visual Prediction

Autoregressive vision language models unify heterogeneous perception tasks but are highly susceptible to compounding errors. On-policy distillation (OPD) bridges the training-inference mismatch by training students on their own rollouts. However, unreliable student predictions, especially early in training, can derail the trajectory and degrade the quality of teacher supervision. While recent interleaved distillation methods allow the teacher to verify and replace student tokens, they primarily rely on rigid ranking metrics rather than exact teacher confidence, and they overlook how intervention decisions can inform token-level supervision. To address this, we introduce Confidence-Aware On-Policy Distillation (CA-OPD), a framework that couples reliable rollout construction with adaptive supervision. CA-OPD utilizes teacher confidence to selectively correct unreliable student transitions, gradually transferring rollout control to the student via a strict-to-relaxed schedule. Crucially, CA-OPD aligns knowledge transfer with these intervention decisions: corrected positions receive direct cross-entropy supervision from the teacher's prediction, while retained positions benefit from the teacher's full predictive distribution. Evaluated in a multi-teacher setting for GUI grounding and optical character recognition, CA-OPD substantially improves the Qwen3.5-0.8B baseline across all six target benchmarks, including gains of 9.509.50 points on ScreenSpot-Pro and 6.726.72 points on OCRBench-v2 English. Controlled studies further show that the gains depend on intervention placement, progressive rollout control, and intervention-aligned supervision, rather than intervention frequency alone.

Menghao Li, Linjie Mu, Haotian Hu +5

Tianjin University · Shanghai Jiao Tong University · StepX

On-Policy Distillation
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Sep 1, 2026

On-Policy Distillation Meets Off-Policy GRPO: Training Compact Instruction-Following Rerankers

Compact instruction-following rerankers are attractive for deployment, but conventional distillation pipelines typically train students by offline imitation of teacher outputs on a fixed set of examples, constraining supervision to the teacher's observed ranking space. We revisit reranker distillation through the lens of reinforcement learning. We propose a two-stage framework combining off-policy teacher optimization with on-policy student distillation. In Stage 1, a 4B teacher reranker is strengthened with off-policy GRPO using LLM-judge feedback on 88K instruction-following examples. In Stage 2, a compact 1B student samples rankings from its own policy and receives soft teacher-derived rewards on those rankings, coupling student exploration with knowledge transfer. Our strongest gains appear under distribution shift. On MAIR-11, the original 11-subset, 869-query evaluation, the proposed student reaches 0.7670 nDCG@6, outperforming offline listwise KD by +4.6 points. Controlled comparisons against offline pairwise RankNet KD and on-policy GKD show that neither changing the offline distillation objective nor moving teacher-distribution matching on-policy reproduces the performance of reward-based on-policy distillation over student-sampled rankings. The advantage persists on MAIR-Full: across all 126 tasks and 9,356 queries, the proposed method obtains the highest task-macro point estimates among the evaluated distillation variants, reaching 0.6808 nDCG@6 and 0.7865 MRR@6. It also exceeds two released 7B RL-trained rerankers on the comparable MAIR-11 evaluation, while the same Stage 2 training procedure consistently improves three architecturally distinct alternative student backbones. On the 9,861-query validation benchmark, the resulting 1B reranker achieves 0.7624 nDCG@6 while providing a favorable quality-efficiency tradeoff relative to larger alternatives.

Vignesh Prabhakar, Jialing Pan, Anil Babu Ankisettipalli

SAP Labs, Palo Alto, CA, USA

Reinforcement LearningLearning to RankLLM RerankingOn-Policy Distillation
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Aug 31, 2026

Reconciling Process Supervision with Outcome-Based Credit in Agentic Policy Optimization

Outcome-based reinforcement learning provides verified feedback for language-model agents, but assigns trajectory-level advantage uniformly to all decisions, yielding coarse credit over long-horizon interactions. On-policy self-distillation offers finer supervision by re-evaluating sampled behavior with privileged information (PI) available only during training. However, fine-grained supervision is not necessarily fine-grained credit: PI-induced likelihood changes describe how additional information alters policy preference, but do not directly determine how an executable action should inherit the verified task outcome. This creates a supervision-credit gap. Privileged signals may be irrelevant to the current interaction state, operate at a token granularity misaligned with executable decisions, and lack the outcome semantics required for reinforcement. We introduce TASPO, which converts privileged supervision into outcome-grounded action credit. TASPO constructs decision-applicable PI from verified successful experience, aggregates PI-induced likelihood shifts at the executable-action level, and converts relative action support into positive, bounded, mean-preserving weights on the original trajectory advantage. Thus, the verified outcome determines the update direction and average scale, while PI only redistributes credit across actions. Across three agentic benchmarks, TASPO improves over GRPO by 10.6% and generalizes better to unseen tasks. Further analysis indicates that TASPO reduces supervision mismatch and that action-level assignment stabilizes the policy optimization process. These findings offer the community another interesting perspective.

Jingxiao Yang, Wangjie Gan, Yingxuan Zhuang +3

Zhejiang University

Agentic RLGroup Relative Policy OptimizationCredit Assignment in RLReinforcement Learning with Verifiable RewardsOn-Policy Distillation
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Aug 31, 2026

Does On-Policy Distillation Really Distill? From Noisy Teacher to Self-Improvement

On-policy distillation (OPD) offers dense token-level supervision as an alternative to the sparse outcome-level advantages of reinforcement learning with verifiable rewards (RLVR). However, the teacher scores student-generated trajectories that are inherently off-policy for it, so the reliability of its supervision, and hence the source of the student's improvement, remains unclear. We quantitatively analyze teacher supervision during OPD training and find substantial noise whose prevalence increases with teacher scale. Surprisingly, the student policy is insensitive to such noise, converging to comparable performance regardless of whether noisy supervision is retained or removed. Does OPD distill at all? By analyzing what drives its gains, we find that learning concentrates on low log-probability tokens, and using a single fixed negative advantage matches the performance of teacher-provided ones. This suggests that OPD works largely by suppressing low log-probability tokens, which requires no teacher. These findings motivate On-Policy Self-Adaptation (OPSA), a supervision-free method using entropy-adaptive negative advantages. It assigns stronger learning signals to high-entropy positions, suppressing tail tokens, and evenly redistributing probability mass among head tokens. Compared with the base Qwen3-1.7B, OPSA improves Avg@32 by 35.41 points on AIME24, corresponding to a 263% relative gain, and more than doubles Pass@32 across all three benchmarks. It also outperforms OPD by 16.77 points in Avg@32 on AIME24. Extensive experiments and analyses across model families and tasks further demonstrate its effectiveness and generalizability.

Yi Ding, Ruqi Zhang

Department of Computer Science, Purdue University, USA

RL for Language ModelsLanguage Model DistillationOn-Policy DistillationLanguage Model Self-ImprovementPolicy Learning
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Aug 30, 2026

Influence-Directed Distillation: Solving the Diversity Bottleneck in Sampled-Token On-Policy Distillation

Sampled-token on-policy distillation (OPD) efficiently transfers capabilities from teacher to student using student-generated tokens, requiring teacher probabilities only for sampled tokens. Yet it frequently suffers from diversity distillation failure: the student's pass@1 improves while its pass@kk plateaus, failing to inherit the teacher's diversity. To explain this, we introduce First-Order Local Entropy Influence, a signed first-order proxy that decouples each update's entropy effect into the teacher--student log-probability gap and the student's local probability structure, and empirically links entropy contraction to negative-influence positions. Motivated by this, we propose Influence-Directed Adaptive On-Policy Distillation (IDA-OPD): rather than relying on costly full-vocabulary Forward-KL objectives, it preserves entropy-expanding updates while replacing entropy-contracting ones with divergence-adaptive advantage shrinkage, using only the teacher's sampled-token log-probability. Experiments on reasoning-oriented distillation show IDA-OPD consistently improves pass@kk, inheriting the teacher's diversity through distillation, matches the strongest teacher-informed methods at strictly lower cost, and broadly maintains vanilla OPD's pass@1, all without full-vocabulary teacher information.

Run Yang, Runpeng Dai, Jie Sun +5

University of North Carolina at Chapel Hill · University of Science and Technology of China · Shanghai University of Finance and Economics

Language Model DistillationOn-Policy DistillationKnowledge Distillation
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Aug 28, 2026

When Teacher Guidance Misleads: Reward-Aligned On-Policy Distillation

On-policy distillation (OPD) has recently emerged as a popular post-training paradigm for large language models (LLMs), providing an efficient way to transfer the knowledge and capabilities of teacher models into student models. However, teacher guidance on student-generated prefixes is not always reliable. Training should optimize the model to generate responses that are more likely to be correct, or equivalently, to get higher outcome rewards. But during OPD, the teacher model may provide guidance that discourages the student from moving toward correct trajectories or moves the student toward incorrect ones, which is misaligned with outcome reward. Such misaligned guidance is unreliable, as it would mislead the optimization process and ultimately degrade model performance. To mitigate misaligned teacher guidance, we propose Reward-Aligned On-Policy Distillation (RA-OPD). The key insight is to keep only trajectories whose induced updates move the student toward correct trajectories or discourage the student from moving toward incorrect ones. Specifically, for each sampled trajectory, RA-OPD checks whether its trajectory-level distillation return is consistent with its outcome reward and then filters out the misaligned trajectories. RA-OPD selects more reliable trajectories to improve student model performance without requiring additional computational cost. We evaluate RA-OPD on math and code benchmarks using models from the Qwen3 family and the DeepSeek-R1 family. Across seven math benchmarks and three code benchmarks, RA-OPD significantly outperforms standard OPD and other tested OPD variants.

Siyuan Gan, Yuhan Li, Xiran Wang +5

State Key Laboratory of Novel Software Technology, Nanjing University, Nanjing, China · Shanghai Artificial Intelligence Laboratory, Shanghai, China

Language Model DistillationOn-Policy DistillationKnowledge Distillation
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Aug 28, 2026

SpikeOPD: Stable On-Policy Distillation for Autoregressive Spiking Language Models

Spiking neural networks (SNNs) offer a path to energy-efficient language modeling through sparse encoding and event-driven computation, but training capable spiking language models from scratch remains difficult. A practical alternative is ANN-to-SNN migration through knowledge distillation (KD), where a pretrained artificial neural network (ANN) teacher supervises an SNN student. Existing migration approaches distill on fixed corpus prefixes, whereas autoregressive inference conditions on self-generated prefixes, creating prefix-source mismatch. It manifests as output-policy mismatch with the ANN teacher and internal spiking-dynamics drift between self-generated and matched corpus prefixes. On-policy distillation (OPD) offers a natural way to mitigate both manifestations by continuing teacher supervision on self-generated prefixes. We evaluate a teacher-only full-KL variant, Vanilla OPD, via a controlled stress test and observe it may suffer from delayed rollout-feedback collapse. This result shows that on-policy coverage alone does not ensure stable adaptation. Motivated by these findings, we propose SpikeOPD, a stable on-policy distillation framework for autoregressive SNNs that learns from self-generated prefixes while maintaining rollout stability. It applies full-KL teacher correction to reduce output-policy mismatch, while matched-prefix policy anchoring constrains policy departure from the frozen reference SNN on the same prefixes. Layerwise spike regularization further limits firing-rate deviations during on-policy adaptation. Across three model scales, SpikeOPD improves average accuracy over the corresponding KD SNNs by 0.8, 1.7, and 2.9 points at 0.125B, 0.35B, and 1.3B, respectively, while preserving their sparse-compute profiles.

Enqiao Lu, Xingrui Yu, Yiwei Fu +7

The Chinese University of Hong Kong, Shenzhen · Agency for Science, Technology and Research (A*STAR), Singapore · Nanyang Technological University, Singapore +3

Spiking Language ModelsSpiking Neural NetworksOn-Policy DistillationKnowledge DistillationLanguage ModelingAutoregressive Language Modeling
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Aug 27, 2026

TTPO: Test-Time Policy Optimization

Recent prominent post-training methods, such as Reinforcement Learning (RL) and On-Policy Self-Distillation (OPSD), have driven rapid progress in mathematical reasoning for large language models, yet their reliance on ground-truth labels precludes test-time training (TTT). Replacing ground truth with majority-vote pseudo-labels is a natural alternative, yet it is fragile: an incorrect vote corrupts the teacher and misleads every token. We observe that this failure mode is asymmetric: rollouts that disagree with the pseudo-label are typically wrong regardless of whether the vote itself is correct. Building on this observation, we propose Test-Time Policy Optimization (TTPO), an asymmetric objective that distills agreeing rollouts via OPSD and penalizes disagreeing rollouts with Grouped RL. Token-level selection further refines both branches: distillation down-weights already-converged positions, while RL penalizes only confident errors. Both updates remain well-grounded even under frequent pseudo-label errors, and majority-vote routing yields tighter self-supervision as the model improves. Without any labels, TTPO matches label-supervised OPSD on five competition-level benchmarks, raises Qwen3-1.7B from 38.0% to 45.2% in TTT, yields +25.2% to +36.4% without thinking, and shows strong cross-task generalization.

Aozhe Wang, Zhengxi Lu, Jianze Wang +8

Zhejiang University · Alibaba Group

Test-Time TrainingTest-Time RLLLM ReasoningSelf-Training for Language ModelsRL for Language Model ReasoningOn-Policy Distillation
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Aug 27, 2026

Self-OPD: On-Policy Distillation for Flow Matching Models without Teacher

On-policy distillation (OPD), which leverages a pre-trained, specialized teacher model to provide dense supervisory signals, has achieved significant success in Large Language Models (LLMs) and has recently been adapted to flow matching models. However, this paradigm suffers from two major issues: First, training a separate, task-specific teacher for every new objective incurs high computational costs. Second, the discrepancy between teacher and student distributions often leads to compounding errors along the generation trajectory. In this paper, we introduce Self-OPD, a teacher-free OPD framework for flow matching models that turns the student's own self-exploration into step-wise supervision. At each timestep, Self-OPD branches the deterministic next-state prediction into KK stochastic SDE candidates, rolls them out with the ODE sampler, and compares their rewards against a deterministic self-reference baseline to obtain normalized advantages. The velocity field is optimized with an all-branch pull-push objective, where high-advantage branches attract the student and low-advantage branches repel it under direction-aware attenuation and SDE-variance normalization. For multi-objective alignment, Self-OPD fuses normalized scores at the reward level, avoiding direct gradient conflict. Experiments on single and mixed reward benchmarks show that Self-OPD outperforms prior RL and OPD methods without task-specific teachers.

Shiyi Zhang, Mushui Liu, Yunze Tong +8

1Tsinghua University · 2Zhejiang University · 3Alibaba Group

Flow MatchingOn-Policy Self-DistillationOn-Policy Distillation
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Aug 27, 2026

Recovering General Capabilities via Uncertainty-Calibrated Multi-Teacher On-Policy Distillation

Specializing large language models to vertical domains improves domain-specific behavior but often degrades general capabilities. We study this trade-off in Multi-Teacher On-Policy Distillation (MOPD), where a specialized model learns from domain and general teachers on its own sampled trajectories. Standard MOPD faces two limitations: ordinary on-policy sampling rarely exposes tokens with large positive teacher--student advantages, and advantage sign alone does not establish whether the proposed update direction is reliable. We propose Uncertainty-Calibrated MOPD (UCMOPD), which addresses these limitations through two complementary mechanisms. Golden-Gain Enhancement combines higher-temperature exploration with a standard-temperature anchor and retains trajectories whose positive learning signal matches or exceeds the prompt-specific anchor. Teacher-Endorsement Filtering then uses centered log-likelihood (CLL) to estimate each retained token's plausibility relative to the teacher's uncertainty and probabilistically preserves updates whose directions are supported by that endorsement. Across role-playing and medical-domain specialization, UCMOPD improves the general-capability average over standard MOPD by 4.48%4.48\% and 7.86%7.86\%, respectively, while maintaining vertical-domain performance. Component ablations and diagnostic analyses support the intended roles of the two mechanisms: exposing and selecting stronger positive signals at the trajectory level and validating update directions through teacher endorsement at the token level.

Ziyuan Liu, Jiao Ou, Jian Liang +2

Kuaishou Technology Beijing, China

Uncertainty-Aware Knowledge DistillationMulti-Teacher Knowledge DistillationOn-Policy DistillationKnowledge Distillation
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Aug 27, 2026

SPEAR: Distilling Domain-Adaptive Reasoning Skeletons via Sequential Symbolic Alignment in Reinforcement Learning

Reinforcement learning-based knowledge distillation has the potential to transfer complex reasoning from teacher to student models, yet it currently faces a critical dilemma: researchers must choose between sparse outcome-based rewards, which provide insufficient logical guidance, or expensive neural Process Reward Models (PRMs) for dense signals. We resolve this by introducing SPEAR (Symbolic Process Evaluation and Alignment Reward), a training-free and plug-and-play process reward method for sequence-level on-policy distillation. SPEAR projects natural-language reasoning traces into domain-adaptive symbolic milestones, providing an efficient proxy for process-level reasoning alignment. By utilizing the longest common subsequence (LCS) to align student explorations with teacher milestones, SPEAR provides a dense, order-aware reward signal that aligns logical consistency without the need for an external neural verifier. Our experiments across math, science, and commonsense reasoning tasks demonstrate that SPEAR effectively bridges the reasoning gap between student and teacher models via sequence-level distillation with efficient dense process rewards. Our code and data are available at: https://github.com/zhuochunli/SPEAR.

Zhuochun Li, Yuelyu Ji, Yiming Zeng +1

University of Pittsburgh, Pittsburgh, USA · University of Connecticut, Storrs, USA

Process Reward ModelsRL for Language Model ReasoningOn-Policy DistillationKnowledge Distillation
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Aug 26, 2026

One Symptom, Three Levers: A Critical Review of On-Policy Self-Distillation

On-policy distillation trains a language model on its own generations while a teacher scores them token by token. It combines the dense supervision of imitation learning with the on-policy sampling of reinforcement learning. But it requires a second, larger model to act as teacher. On-Policy Self-Distillation (OPSD) removes that cost. The teacher is the model itself, conditioned on privileged information the student will not have at test time, such as a reference solution, a plan, or environment feedback. The teacher is no stronger than the student, only better informed. Early results were promising, with accuracy comparable to reinforcement learning at a fraction of the generated tokens. But the same asymmetry that produces the signal also biases it. One failure mode now dominates the field: collapse, the progressive narrowing of the set of reasoning paths the model can produce. Collapse is not specific to OPSD, though privileged information aggravates it. This review treats collapse as a symptom governed by three levers: (i) where the signal is applied, that is, how tokens are weighted; (ii) what the teacher is shown, that is, the nature of the privileged information; and (iii) when the signal changes, that is, the teacher's dynamics and the decay of guidance. We restrict our scope to mathematical reasoning, where the method originated and where its failure modes are best documented. We report no new experiments. The contribution is structural: a shared vocabulary for phenomena named differently across papers, and a clear line between what is settled and what is still disputed.

Justin Robert, Raheel Qader

OVHai LLM

On-Policy Self-DistillationOn-Policy DistillationMode Collapse
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Aug 26, 2026

A Token-Level Analysis of Sampled-Token Reverse-KL On-Policy Distillation

On-policy distillation (OPD) supervises a student on its own trajectories with token-level signals from a frozen teacher, yet how a sampled loss allocates updates across tokens remains poorly understood. We analyze the gradient of the per-token K2 estimator of reverse KL with respect to the student logits. The ℓ1\ell_1 norm of this gradient factorizes into the absolute teacher--student log-probability gap and a student-side softmax factor that grows as the sampled token becomes less likely under the student. In our math-distillation runs, these per-token norms are highly non-uniform: low-student-probability tokens account for a disproportionate share of their sum and are also enriched in large teacher--student gaps. As a lightweight intervention suggested by this analysis, we study Surprise-aware Reweighting (SuRe), a detached, bounded weighting rule that further amplifies this existing allocation. Across two Qwen3 student scales, SuRe improves several math metrics over vanilla OPD and shows no clear degradation on the selected out-of-domain benchmarks. Our primary contribution is therefore a gradient-level characterization of reverse-KL OPD trained with the K2 estimator, with SuRe as one empirical instantiation.

Bing Shao, Jiazheng Zhang, Long Ma +13

College of Computer Science and Artificial Intelligence, Fudan University

Language Model DistillationOn-Policy DistillationKnowledge DistillationKullback-Leibler Divergence
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Aug 25, 2026

D3^3-MOPD: Dynamic Domain ScheDuling for Efficient Multi-Teacher Distillation

Multi-teacher on-policy distillation (MOPD) distills several domain-expert teachers into a single student by minimizing per-domain reverse-KL divergence on the student's own rollouts. Existing approaches typically fix the per-domain data mixture before training, overlooking the fact that different domains converge at substantially different rates: some plateau early while others continue to improve throughout the training budget. A fixed mixture therefore wastes compute on fast-converging domains and undertrains slower-converging ones. To address this, we propose D3^3-MOPD (Dynamic Domain ScheDuling for MOPD), a zero-overhead scheduler that repurposes the per-domain reverse-KL signal already produced during training to adapt the domain mixture online. Running asynchronously outside the training process, an off-process watcher periodically tracks each domain's KL trajectory, estimates remaining headroom and current improvement rate, and accordingly adjusts the domain sampling ratios without altering the core training loop. Our D3^3-MOPD scales naturally to arbitrary numbers of domains, and the expected benefit grows as more domains introduce more diverse convergence patterns for the scheduler to exploit. On a Qwen3.6-35B-A3B student distilled from four domain-expert teachers, D3^3-MOPD closes 97% of the average student-to-teacher performance gap, compared with 63% for vanilla MOPD, reaches the same peak performance with an approximately 3×\times reduction in rollout steps, and surpasses the specialist teachers on three of seven benchmarks.

Zechen Sun, Zhiwei Zhang, Fei Zhao +7

AllSpark Team

Adaptive SamplingLanguage Model DistillationMulti-Teacher Knowledge DistillationOn-Policy Distillation
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Aug 25, 2026

On-policy Distillation with Verifiable Reward

Reinforcement Learning with Verifiable Rewards (RLVR) and on-policy distillation (OPD) have become two widely adopted paradigms for post-training large language models. However, RLVR suffers from sparse task-level feedback, while OPD provides dense token-level guidance but ignores trajectory correctness, limiting its performance to that of the teacher. Combining them is a promising direction: OPD supplies dense supervisory signals, while RLVR provides task-level correctness. Nevertheless, existing integrations often rely on weighted combination or heuristic switching, introducing extra hyperparameters and trade-offs. We propose On-policy Distillation with Verifiable Reward (OPDVR), a simple yet effective method that seamlessly combines OPD and RLVR without adding any hyperparameters. We first reformulate the implicit reward of sampled-token OPD based on trajectory correctness, then apply a ReLU gating mechanism to ensure that correct trajectories receive non-negative rewards and incorrect ones receive non-positive rewards---thereby aligning the distillation signal with task success while preserving the teacher's distributional guidance. Furthermore, our modification transforms sampled-token OPD into a proper RLVR method, making it readily combinable with any policy gradient algorithm, such as GRPO. Experiments on six reasoning benchmarks show that OPDVR consistently outperforms standard OPD. Our code is available at https://github.com/LeapLabTHU/OPDVR.

Wenze Lin, Jiale Zhao, Xitai Jiang +5

LeapLab, Tsinghua University · Qiuzhen College, Tsinghua University · Beihang University +2

RL for Language Model ReasoningReinforcement Learning with Verifiable RewardsOn-Policy DistillationRL Post-Training
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Aug 25, 2026

On-Policy Self-Distillation in Diffusion Models

Reinforcement learning can align diffusion models with human preferences and task-specific objectives, but endpoint rewards do not specify how an intermediate denoising prediction should change. We introduce DiffusionOPSD as an on-policy self-distillation framework that converts image-level reward guidance into explicit targets for clean-output predictions at sampled queries. At each outer iteration, a frozen behavior policy generates trajectories and supplies query states and anchors. Reward gradients construct bounded positive and negative targets around each anchor. The trainable policy fits these targets as detached supervision through finite fitting before an exponential moving average update refreshes the behavior policy. This setup lets us measure target construction and finite realization separately. Controlled same-query experiments show that larger target-construction gains do not necessarily translate into larger realized gains after a single fitting update. Across SD 3.5-M and the step-distilled Z-Image-Turbo, our approach achieves the best final held-out scores in 19 of 20 reward-matched settings across two backbones and ten evaluators. It outperforms the strongest competing method by up to 44.0% and reduces training GPU-hours relative to DiffusionNFT by 40% on SD 3.5-M and 63% on Z-Image-Turbo. These results support on-policy self-distillation as an efficient and analyzable approach to diffusion post-training by converting image-level reward guidance into explicit and continually refreshed intermediate supervision, thereby opening a path toward more efficient and diagnosable alignment.

Wei Zhou, Xiongwei Zhu, Lingdong Kong +14

Diffusion Model AlignmentOn-Policy Self-DistillationDiffusion Model Fine-TuningOn-Policy DistillationRL for Diffusion Models
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Aug 25, 2026

OPDSearch+: On-Policy Distillation with RL Refinement for Search-Augmented Reasoning

Search-augmented reasoning remains difficult for small language models. On-policy distillation (OPD) from trained teachers offers a promising direction, but suffers from two issues: (1) high-quality multi-turn search trajectories depend on dynamic retriever responses, making SFT data prohibitively expensive to collect at scale; (2) task-specifically trained teachers incur substantial training cost, while directly applying OPD with an off-the-shelf teacher without task-specific fine-tuning constrains the student to the teacher's performance ceiling and suffers from severe training instability. We propose OPDSearch+, the first distillation paradigm that requires no teacher fine-tuning for search-augmented reasoning. We investigate the role of a frozen off-the-shelf instruct model as the teacher in on-policy distillation, and reveal a key insight: the teacher reshapes the student's policy distribution so that subsequent RL converges to a superior solution that RL alone cannot reach. In stage one, the student interacts with a live search engine and is distilled via a per-position forward KL objective, transferring reasoning decomposition and evidence integration skills without any task-specific teacher training. In stage two, RL refines the distilled student from a richer behavioral foundation, achieving performance that RL alone cannot reach from scratch. Across seven QA benchmarks, OPDSearch+ with a 3B model consistently outperforms all prior 3B RL baselines, achieving gains of 13.1% on HotpotQA and 8.5% on 2WikiMultihopQA.

Qinglin Ye, Zhiyuan Gu, Jingjie Xia +6

University of Chinese Academy of Sciences · Institute of Computing Technology, Chinese Academy of Sciences · Institute of Automation, Chinese Academy of Sciences +5

On-Policy DistillationLLM ReasoningKnowledge DistillationRL for Language Model ReasoningMulti-Hop QA
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Aug 25, 2026

CataOPD: Catalytic On-Policy Distillation for Large Language Model Reasoning

Reinforcement learning (RL) and on-policy distillation (OPD) are two representative paradigms for improving large language model reasoning. However, when no correct trajectory is sampled, RL lacks a positive correctness signal, while OPD remains constrained by the reasoning trajectories reachable under the student's on-policy distribution. Therefore, we propose CataOPD, where the teacher acts as a catalyst rather than a target, expanding reachability while internalizing verified student-produced trajectories into a catalyst-free policy. Self-Rescue Routing uses empirically all-failed groups as routing signals rather than teacher-intervention triggers, first seeking correct trajectories through additional on-policy self-sampling. For problems unresolved after self-rescue, Catalytic-Guided Self-Resolution uses catalytic guidance to elicit a verified student-produced trajectory in the guided student distribution. Barrier-Weighted Internalization weights tokens by guided-to-unguided log-probability gaps, focusing updates on decisive tokens difficult without guidance. Experimental results show that CataOPD outperforms current baselines, extends independent student reasoning to still-unrecovered problems, and improves out-of-distribution generalization under catalyst-free inference. Our project is available at https://github.com/QwenQKing/CataOPD.

Wenjin Liu, Chenxi Wang, Jiapu Wang +3

Nanyang Technological University, College of Computing and Data Science, Singapore · Hithink Research, Code Generation Department, Hangzhou, China · Nanjing University of Science and Technology, School of Computer Science and Technology, Nanjing, China

On-Policy DistillationRL for Language Model ReasoningLLM-Guided RL
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Aug 23, 2026

WAM-OPD: Joint Video-Action Supervision for World Action Model Post-Training with On-Policy Distillation

World Action Models (WAMs) generate both future video and robot actions, offering two connected outputs for post-training supervision. How can a pretrained WAM learn from a stronger Teacher on the histories it encounters during execution? We present WAM-OPD, which collects Student rollout histories and queries a Teacher for paired video and action targets. The Student learns from both targets while retaining its one-step video and action generation at deployment. Across 12 RoboTwin 2.0 tasks, WAM-OPD improves average success from 33.8% to 65.7%; across four real-robot tasks, it improves average success from 51.4% to 64.6%. With the collected Student histories held fixed, joint video-action supervision achieves the highest observed success on all three ablation tasks, while either modality alone also improves performance. A separate comparison with Teacher-generated histories finds task-dependent differences between the two history sources. These results demonstrate the value of paired video-action supervision for improving WAM policies without increasing their deployed sampling budget.

Liuhaichen Yang, Zhengyang Zhong, Hanshang Zhu +13

University College London · Shanghai Jiao Tong University · The University of Manchester +3

World Action ModelsAction-Conditioned World ModelsRobotic ManipulationOn-Policy Distillation
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