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

arXiv: https://arxiv.org/abs/2608.31046 · HTML: https://mlsanity.com/paper/2608.31046/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 35 of its 43 references that are in the map.
- First posted on arXiv 31 Aug 2026.

## Placed in

- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 30 of 35)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [VL-Rethinker: Incentivizing Self-Reflection of Vision-Language Models with Reinforcement Learning](https://mlsanity.com/paper/2504.08837/) (2025)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [SFT or RL? An Early Investigation into Training R1-Like Reasoning Large Vision-Language Models](https://mlsanity.com/paper/2504.11468/) (2025)
- [Learning to Reason without External Rewards](https://mlsanity.com/paper/2505.19590/) (2025)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [Self-Distilled RLVR](https://mlsanity.com/paper/2604.03128/) (2026)
- [Right Question is Already Half the Answer: Fully Unsupervised LLM Reasoning Incentivization](https://mlsanity.com/paper/2504.05812/) (2025)
- [TIP: Token Importance in On-Policy Distillation](https://mlsanity.com/paper/2604.14084/) (2026)
- [MOPD: Multi-Teacher On-Policy Distillation for Capability Integration in LLM Post-Training](https://mlsanity.com/paper/2606.30406/) (2026)
- [Uni-OPD: Unifying On-Policy Distillation with a Dual-Perspective Recipe](https://mlsanity.com/paper/2605.03677/) (2026)
- [Embarrassingly Simple Self-Distillation Improves Code Generation](https://mlsanity.com/paper/2604.01193/) (2026)
- [Rethinking On-Policy Self-Distillation for Thinking Models](https://mlsanity.com/paper/2607.05184/) (2026)
- [Asymmetric On-Policy Distillation: Bridging Exploitation and Imitation at the Token Level](https://mlsanity.com/paper/2605.06387/) (2026)
- [Trust Region On-Policy Distillation](https://mlsanity.com/paper/2606.01249/) (2026)
- [On the Position Bias of On-Policy Distillation](https://mlsanity.com/paper/2606.22600/) (2026)

## Built on by (most cited first, 11 of 11)

- [1% of Tokens Can Be Enough: On Gradient Estimation in On-Policy Distillation](https://mlsanity.com/paper/2609.24432/) (2026)
- [Understanding On-Policy Distillation: A Mechanistic Interpretability Perspective via Sparse Crosscoders](https://mlsanity.com/paper/2609.35210/) (2026)
- [Thinking Leakage: A Causal Audit of NoThink Post-Training in Hybrid Reasoning Models](https://mlsanity.com/paper/2609.28682/) (2026)
- [Expected Reasoning-Step Return Unifies On-Policy Learning from Rewards and Teachers](https://mlsanity.com/paper/2609.32674/) (2026)
- [Surprising Success, Repeated Failure: Entropy-Guided Credit Assignment for Exploration in LLM Reasoning](https://mlsanity.com/paper/2609.33781/) (2026)
- [PIVOT: Pivot-Aware On Policy Self Distillation for Multi-Turn VLM Agents](https://mlsanity.com/paper/2609.35303/) (2026)
- [Dr. OPD: Learning What to Follow for Optimal On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2609.38025/) (2026)
- [Improving OCR Faithfulness via Gated and Attenuated On-Policy Distillation](https://mlsanity.com/paper/2609.38282/) (2026)
- [Rethinking Self-Distillation for Multi-Teacher Capability Merging](https://mlsanity.com/paper/2610.04272/) (2026)
- [On-Policy Distillation Teaches New Skills but Not New Knowledge](https://mlsanity.com/paper/2610.09639/) (2026)
- [JustOPD: On-Policy Distillation from Autoregressive to Diffusion Language Models](https://mlsanity.com/paper/2610.17397/) (2026)

## Abstract (arXiv)

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 textttQwen3-1.7B, 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.