d-OPSD reframes on-policy self-distillation for dLLMs via suffix conditioning from self-generated answers and step-level supervision, outperforming RLVR and SFT on reasoning benchmarks with ~10% of the optimization steps.
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Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe
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abstract
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.
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OmniOPD replaces token-level logit matching in on-policy distillation with Monte Carlo chunk-level semantic verification and a peak-entropy scheduler.
Self-Policy Distillation extracts a capability subspace from model gradients on correctness tokens, projects KV activations into it for self-generation, and fine-tunes LLMs to achieve up to 13-16% gains over baselines without external signals.
Decoupling prefix source from token-level KL direction in autoregressive sequence KL yields four objectives unifying SFT, DAgger, offline RL and OPD, with KL mixing and entropy-gated curriculum improving math reasoning accuracy and shortening responses.
Distillation signals align better with ideal updates on incorrect student rollouts than correct ones, with optimal teacher context depending on student capacity and task.
On-policy distillation has an extrapolation cliff at closed-form lambda*(p,b,c) set by teacher modal probability, warm-start mass, and clip strength, past which training shifts from format-preserving to format-collapsing.
vOPD stabilizes on-policy distillation gradients by subtracting a closed-form per-token negative reverse KL baseline as a detached control variate, preserving unbiasedness while lowering variance and matching expensive full-vocabulary methods.
Rubric-based on-policy distillation allows training student models using only teacher responses by generating scoring rubrics from contrasts and using them for on-policy optimization, achieving superior performance and up to 10x better sample efficiency than logit-based approaches.
MAD-OPD recasts on-policy distillation teachers as a debating collective to supply better supervision, lifting agentic and code performance over single-teacher OPD across multiple model sizes.
GUI-SD introduces on-policy self-distillation with visually enriched privileged context and entropy-guided weighting, outperforming GRPO and naive OPSD on six GUI grounding benchmarks while improving training efficiency.
Position bias in on-policy distillation degrades later-token supervision; IW-OPD weights tokens by accumulated discrepancy, yielding faster convergence and up to 6.9 point gains on AIME-2025.
DASD improves math reasoning in LLMs by adaptively directing self-distillation based on per-token entropy to balance exploration and step accuracy, outperforming prior self-distillation and RLVR baselines on six benchmarks.
Anti-Self-Distillation reverses self-distillation signals via PMI to fix overconfidence on structural tokens, matching GRPO baseline accuracy 2-10x faster with up to 11.5 point gains across 4B-30B models.
SOD reweights on-policy distillation strength step-by-step using divergence to stabilize tool use in small language model agents, yielding up to 20.86% gains and 26.13% on AIME 2025 for a 0.6B model.
SimCT enlarges the supervision space in cross-tokenizer on-policy distillation using short jointly tokenizable multi-token continuations, producing consistent gains over shared-token baselines on math and code benchmarks.
Uni-OPD unifies on-policy distillation across LLMs and MLLMs with dual-perspective strategies that promote student exploration and enforce order-consistent teacher supervision based on outcome rewards.
CoPD integrates multiple expert capabilities by running parallel RLVR training with bidirectional online policy distillation among experts, outperforming mixed RLVR and sequential OPD while surpassing domain-specific experts on text-image-video reasoning.
Truncated and progressively lengthening rollouts in on-policy distillation match full-rollout performance on mathematical reasoning while using as little as 10% of the horizon and improving efficiency up to 3x.
TRB introduces a KL-trust-region warmup for on-policy distillation that blends toward teacher behavior early in training and anneals to zero, reporting the highest average performance across two math-reasoning distillation experiments.
A linear relationship between initial student-self-teacher performance gap and OPSD improvement provides a predictive law across contexts and model families.
f-OPD decomposes on-policy distillation drift into rollout and supervision components, then applies a sample-level freshness score to adaptively limit stale data influence and stabilize long-horizon agent training.
Sparse rewards on capable teachers for exploration followed by dense distillation to students outperforms direct sparse reward application like GRPO on the deployment model.
On-policy distillation gains efficiency from early foresight in module allocation and update directions, which the proposed EffOPD method exploits for 3x faster training with comparable performance.
BRTS improves on-policy distillation by sampling multiple teacher rollouts and selecting the best one via a correctness-first then alignment priority rule, yielding gains on AIME and AMC math benchmarks.
citing papers explorer
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Learning from the Self-future: On-policy Self-distillation for dLLMs
d-OPSD reframes on-policy self-distillation for dLLMs via suffix conditioning from self-generated answers and step-level supervision, outperforming RLVR and SFT on reasoning benchmarks with ~10% of the optimization steps.
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OmniOPD: Logit-Free On-Policy Distillation via Speculative Verification
OmniOPD replaces token-level logit matching in on-policy distillation with Monte Carlo chunk-level semantic verification and a peak-entropy scheduler.
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Self-Policy Distillation via Capability-Selective Subspace Projection
Self-Policy Distillation extracts a capability subspace from model gradients on correctness tokens, projects KV activations into it for self-generation, and fine-tunes LLMs to achieve up to 13-16% gains over baselines without external signals.
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Decoupling KL and Trajectories: A Unified Perspective for SFT, DAgger, Offline RL, and OPD in LLM Distillation
Decoupling prefix source from token-level KL direction in autoregressive sequence KL yields four objectives unifying SFT, DAgger, offline RL and OPD, with KL mixing and entropy-gated curriculum improving math reasoning accuracy and shortening responses.
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Unmasking On-Policy Distillation: Where It Helps, Where It Hurts, and Why
Distillation signals align better with ideal updates on incorrect student rollouts than correct ones, with optimal teacher context depending on student capacity and task.
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The Extrapolation Cliff in On-Policy Distillation of Near-Deterministic Structured Outputs
On-policy distillation has an extrapolation cliff at closed-form lambda*(p,b,c) set by teacher modal probability, warm-start mass, and clip strength, past which training shifts from format-preserving to format-collapsing.
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KL for a KL: On-Policy Distillation with Control Variate Baseline
vOPD stabilizes on-policy distillation gradients by subtracting a closed-form per-token negative reverse KL baseline as a detached control variate, preserving unbiasedness while lowering variance and matching expensive full-vocabulary methods.
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Rubric-based On-policy Distillation
Rubric-based on-policy distillation allows training student models using only teacher responses by generating scoring rubrics from contrasts and using them for on-policy optimization, achieving superior performance and up to 10x better sample efficiency than logit-based approaches.
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MAD-OPD: Breaking the Ceiling in On-Policy Distillation via Multi-Agent Debate
MAD-OPD recasts on-policy distillation teachers as a debating collective to supply better supervision, lifting agentic and code performance over single-teacher OPD across multiple model sizes.
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Learn where to Click from Yourself: On-Policy Self-Distillation for GUI Grounding
GUI-SD introduces on-policy self-distillation with visually enriched privileged context and entropy-guided weighting, outperforming GRPO and naive OPSD on six GUI grounding benchmarks while improving training efficiency.
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On the Position Bias of On-Policy Distillation
Position bias in on-policy distillation degrades later-token supervision; IW-OPD weights tokens by accumulated discrepancy, yielding faster convergence and up to 6.9 point gains on AIME-2025.
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Tailoring Teaching to Aptitude: Direction-Adaptive Self-Distillation for LLM Reasoning
DASD improves math reasoning in LLMs by adaptively directing self-distillation based on per-token entropy to balance exploration and step accuracy, outperforming prior self-distillation and RLVR baselines on six benchmarks.
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Anti-Self-Distillation for Reasoning RL via Pointwise Mutual Information
Anti-Self-Distillation reverses self-distillation signals via PMI to fix overconfidence on structural tokens, matching GRPO baseline accuracy 2-10x faster with up to 11.5 point gains across 4B-30B models.
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SOD: Step-wise On-policy Distillation for Small Language Model Agents
SOD reweights on-policy distillation strength step-by-step using divergence to stabilize tool use in small language model agents, yielding up to 20.86% gains and 26.13% on AIME 2025 for a 0.6B model.
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SimCT: Recovering Lost Supervision for Cross-Tokenizer On-Policy Distillation
SimCT enlarges the supervision space in cross-tokenizer on-policy distillation using short jointly tokenizable multi-token continuations, producing consistent gains over shared-token baselines on math and code benchmarks.
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Uni-OPD: Unifying On-Policy Distillation with a Dual-Perspective Recipe
Uni-OPD unifies on-policy distillation across LLMs and MLLMs with dual-perspective strategies that promote student exploration and enforce order-consistent teacher supervision based on outcome rewards.
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Co-Evolving Policy Distillation
CoPD integrates multiple expert capabilities by running parallel RLVR training with bidirectional online policy distillation among experts, outperforming mixed RLVR and sequential OPD while surpassing domain-specific experts on text-image-video reasoning.
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Are Full Rollouts Necessary for On-Policy Distillation?
Truncated and progressively lengthening rollouts in on-policy distillation match full-rollout performance on mathematical reasoning while using as little as 10% of the horizon and improving efficiency up to 3x.
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Trust-Region Behavior Blending for On-Policy Distillation
TRB introduces a KL-trust-region warmup for on-policy distillation that blends toward teacher behavior early in training and anneals to zero, reporting the highest average performance across two math-reasoning distillation experiments.
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A Predictive Law for On-Policy Self-Distillation From World Feedback
A linear relationship between initial student-self-teacher performance gap and OPSD improvement provides a predictive law across contexts and model families.
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$\boldsymbol{f}$-OPD: Stabilizing Long-Horizon On-Policy Distillation with Freshness-Aware Control
f-OPD decomposes on-policy distillation drift into rollout and supervision components, then applies a sample-level freshness score to adaptively limit stale data influence and stabilize long-horizon agent training.
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Beyond GRPO and On-Policy Distillation: An Empirical Sparse-to-Dense Reward Principle for Language-Model Post-Training
Sparse rewards on capable teachers for exploration followed by dense distillation to students outperforms direct sparse reward application like GRPO on the deployment model.
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Learning to Foresee: Unveiling the Unlocking Efficiency of On-Policy Distillation
On-policy distillation gains efficiency from early foresight in module allocation and update directions, which the proposed EffOPD method exploits for 3x faster training with comparable performance.
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On-Policy Distillation with Best-of-N Teacher Rollout Selection
BRTS improves on-policy distillation by sampling multiple teacher rollouts and selecting the best one via a correctness-first then alignment priority rule, yielding gains on AIME and AMC math benchmarks.
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VISD: Enhancing Video Reasoning via Structured Self-Distillation
VISD proposes structured self-distillation with a multi-dimensional judge model and direction-magnitude decoupling to improve token-level credit assignment and convergence speed in VideoLLM reasoning training.
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Internalize the Temperature: On-Policy Self-Distillation as Policy Reheater for Reinforcement Learning
TS-OPSD internalizes temperature via on-policy self-distillation to reheat entropy-collapsed RL policies in LLMs, providing stronger initialization for further training than continued RL or rollout temperature adjustment.
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A Brief Overview: On-Policy Self-Distillation In Large Language Models
This overview paper explains the conceptual foundations and design principles of On-Policy Self-Distillation for large language models from a beginner's perspective.
- Adapting the Interface, Not the Model: Runtime Harness Adaptation for Deterministic LLM Agents
- Don't Guess, Just Ask: Resolving Ambiguity in Referring Segmentation via Multi-turn Clarification
- Prune-OPD: Efficient and Reliable On-Policy Distillation for Long-Horizon Reasoning