# On-Policy Distillation with Negative-Policy Rollouts

arXiv: https://arxiv.org/abs/2610.07874 · HTML: https://mlsanity.com/paper/2610.07874/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 27 of its 44 references that are in the map.
- First posted on arXiv 6 Oct 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, 27 of 27)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Orca: Progressive Learning from Complex Explanation Traces of GPT-4](https://mlsanity.com/paper/2306.02707/) (2023)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Gemma 4 Technical Report](https://mlsanity.com/paper/2607.02770/) (2026)
- [MiMo-V2-Flash Technical Report](https://mlsanity.com/paper/2601.02780/) (2026)
- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)
- [Entropy-Aware On-Policy Distillation of Language Models](https://mlsanity.com/paper/2603.07079/) (2026)
- [AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset](https://mlsanity.com/paper/2504.16891/) (2025)
- [DistiLLM: Towards Streamlined Distillation for Large Language Models](https://mlsanity.com/paper/2402.03898/) (2024)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [MiniLLM: On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2306.08543/) (2023)
- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [REASONING GYM: Reasoning Environments for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2505.24760/) (2025)
- [Olmo 3](https://mlsanity.com/paper/2512.13961/) (2025)
- [OpenCodeReasoning: Advancing Data Distillation for Competitive Coding](https://mlsanity.com/paper/2504.01943/) (2025)
- [SuperGPQA: Scaling LLM Evaluation across 285 Graduate Disciplines](https://mlsanity.com/paper/2502.14739/) (2025)
- [Lightning OPD: Efficient Post-Training for Large Reasoning Models with Offline On-Policy Distillation](https://mlsanity.com/paper/2604.13010/) (2026)
- [The Delta Learning Hypothesis: Preference Tuning on Weak Data can Yield Strong Gains](https://mlsanity.com/paper/2507.06187/) (2025)
- [Weak-to-Strong Generalization via Direct On-Policy Distillation](https://mlsanity.com/paper/2607.05394/) (2026)
- [Pass the Baton: Trajectory-Relayed On-Policy Distillation](https://mlsanity.com/paper/2607.26057/) (2026)
- [On-Policy Delta Distillation](https://mlsanity.com/paper/2607.15161/) (2026)
- [Lightning OPD 2.0: Mitigating Style Bias in Cross-Teacher On-Policy Distillation for Large Reasoning Models](https://mlsanity.com/paper/2607.28449/) (2026)

## Abstract (arXiv)

On-policy distillation (OPD) has been widely studied as a post-training method in which a student model obtains token-level supervision from a stronger teacher on its own rollouts. Recent studies have improved OPD through alternative distillation reward formulations and teacher configurations, while the objective of distillation remains centered on mimicking the teacher. However, when a stronger teacher has limited distributional overlap with the student, such positive guidance can provide insufficient learning signals. In this work, we introduce Negative-Policy OPD (NP-OPD), which complements teacher supervision with rollouts from a lower-performing, lower-capability negative policy that serves as a negative reference for the student. Rather than modifying the distillation reward formulation, NP-OPD introduces the negative policy at the rollout stage, continuously supplying tokens preferred by the negative policy over the teacher so that they remain exposed to teacher supervision throughout training. This provides an explicit negative signal through negative-policy rollouts while preserving the positive teacher supervision used in OPD. Through extensive experiments, we show that NP-OPD improves OPD across model scales, generation modes, reasoning domains, and different OPD variants. Furthermore, our analyses show that NP-OPD effectively suppresses tokens preferred by the negative policy over the teacher and moves the student away from the negative policy. These results support our design of introducing negative signals through negative-policy rollouts and provide new insight into the role of the rollout policy in OPD. Code will be available at https://github.com/naver-ai/np-opd.