# Purified OPSD: On-Policy Self-Distillation Without Losing How to Think

arXiv: https://arxiv.org/abs/2607.02234 · HTML: https://mlsanity.com/paper/2607.02234/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 27 of its 37 references that are in the map.
- First posted on arXiv 2 Jul 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- 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)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [2 OLMo 2 Furious](https://mlsanity.com/paper/2501.00656/) (2024)
- [Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond](https://mlsanity.com/paper/2503.10460/) (2025)
- [Distilling System 2 into System 1](https://mlsanity.com/paper/2407.06023/) (2024)
- [Stream of Search (SoS): Learning to Search in Language](https://mlsanity.com/paper/2404.03683/) (2024)
- [Why Does Self-Distillation (Sometimes) Degrade the Reasoning Capability of LLMs?](https://mlsanity.com/paper/2603.24472/) (2026)
- [Self-Distillation Zero: Self-Revision Turns Binary Rewards into Dense Supervision](https://mlsanity.com/paper/2604.12002/) (2026)
- [RedStar: Does Scaling Long-CoT Data Unlock Better Slow-Reasoning Systems?](https://mlsanity.com/paper/2501.11284/) (2025)
- [Deconstructing Long Chain-of-Thought: A Structured Reasoning Optimization Framework for Long CoT Distillation](https://mlsanity.com/paper/2503.16385/) (2025)
- [Unveiling the Key Factors for Distilling Chain-of-Thought Reasoning](https://mlsanity.com/paper/2502.18001/) (2025)
- [R1-Compress: Long Chain-of-Thought Compression via Chunk Compression and Search](https://mlsanity.com/paper/2505.16838/) (2025)
- [Distribution-Aligned Sequence Distillation for Superior Long-CoT Reasoning](https://mlsanity.com/paper/2601.09088/) (2026)
- [Skip-Thinking: Chunk-wise Chain-of-Thought Distillation Enable Smaller Language Models to Reason Better and Faster](https://mlsanity.com/paper/2505.18642/) (2025)
- [Rethinking Generalization in Reasoning SFT: A Conditional Analysis on Optimization, Data, and Model Capability](https://mlsanity.com/paper/2604.06628/) (2026)
- [Feature Extraction and Steering for Enhanced Chain-of-Thought Reasoning in Language Models](https://mlsanity.com/paper/2505.15634/) (2025)
- [Through the Valley: Path to Effective Long CoT Training for Small Language Models](https://mlsanity.com/paper/2506.07712/) (2025)
- [Beyond Scaling Law: A Data-Efficient Distillation Framework for Reasoning](https://mlsanity.com/paper/2508.09883/) (2025)
- [A Brief Overview: On-Policy Self-Distillation In Large Language Models](https://mlsanity.com/paper/2605.18141/) (2026)

## Built on by (most cited first, 30 of 31)

- [Recursive Self-Improvement in AI: From Bounded Self-Refinement to Autonomous Research Loops](https://mlsanity.com/paper/2607.07663/) (2026)
- [Privileged Solutions or Context-Induced Teacher Behavior? Dissecting On-Policy Self-Distillation](https://mlsanity.com/paper/2608.09228/) (2026)
- [Is More Privileged Information Better? From Solution Traces to Problem-Solving Structure in Self-Distilled Reasoning](https://mlsanity.com/paper/2608.01589/) (2026)
- [Rethinking Privileged Information in On-Policy Self-Distillation](https://mlsanity.com/paper/2608.18271/) (2026)
- [Agentic Reinforcement Learning with Observation-Calibrated Self-Distillation](https://mlsanity.com/paper/2608.04788/) (2026)
- [DASH: Divergence-Adaptive Supervision Horizons for On-Policy Self-Distillation of Reasoning Models](https://mlsanity.com/paper/2608.06243/) (2026)
- [Diagnosing and Mitigating Thinking Collapse in On-Policy Self-Distillation](https://mlsanity.com/paper/2607.10805/) (2026)
- [Privileged Likelihood Is Not Automatically Value: Three Checks for Token Credit in On-Policy Self-Distillation](https://mlsanity.com/paper/2608.09263/) (2026)
- [Learning When to Trust via Selective Context Preference Optimization](https://mlsanity.com/paper/2608.06377/) (2026)
- [Matching Supervision to the Student's Learning Capacity: A Unified Framework for On-Policy Self-Distillation](https://mlsanity.com/paper/2608.08176/) (2026)
- [DAPD: Dual-Anchored Policy Distillation](https://mlsanity.com/paper/2608.01735/) (2026)
- [What Does Privileged Information Add to On-Policy Self-Distillation?](https://mlsanity.com/paper/2609.20612/) (2026)
- [Overcoming Scaling Limits in On-Policy Self-Distillation for LLM Reasoning](https://mlsanity.com/paper/2609.37915/) (2026)
- [Activation-Conditioned Self-Distillation](https://mlsanity.com/paper/2609.38342/) (2026)
- [One Symptom, Three Levers: A Critical Review of On-Policy Self-Distillation](https://mlsanity.com/paper/2608.25936/) (2026)
- [VISTA: Verifier-Informed Student-to-Teacher Adaptation for On-Policy Self-Distillation](https://mlsanity.com/paper/2608.28306/) (2026)
- [Aha-Flow Distillation: Flow Markers Matter in LLM Reasoning](https://mlsanity.com/paper/2609.07036/) (2026)
- [PSD: Pseudo Self-Distillation of Memory Representation Capabilities for LLM Agents](https://mlsanity.com/paper/2609.23449/) (2026)
- [MM-OPD: Towards One More Bottleneck Between Perception and Reasoning](https://mlsanity.com/paper/2609.32690/) (2026)
- [Can We Trust the Teacher? Decoupled Credit Direction-Magnitude for Self-Distillation](https://mlsanity.com/paper/2609.34848/) (2026)
- [Train Ahead, Distill Back: Bootstrapping On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2609.37132/) (2026)
- [Diagnosing On-Policy Self-Distillation for Reasoning Language Models](https://mlsanity.com/paper/2609.39118/) (2026)
- [Better Supervision Is Nearby: Neighborhood On-Policy Self-Distillation](https://mlsanity.com/paper/2609.39687/) (2026)
- [The Missing Primitive: Diagnosing and Repairing Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2610.02191/) (2026)
- [E2-OPSD: Taming Entropy Overshoot in On-Policy Self-Distillation](https://mlsanity.com/paper/2610.05048/) (2026)
- [Outcome-Guided On-Policy Self-Distillation](https://mlsanity.com/paper/2610.05070/) (2026)
- [Off-Policy Merging Beats On-Policy Self-Distillation for Continual Learning](https://mlsanity.com/paper/2610.05872/) (2026)
- [Distilling Routed 3D Privilege for Spatial Reasoning in Vision-Language Models](https://mlsanity.com/paper/2610.12355/) (2026)
- [PreSO: Privileged Representation Isolation for On-Policy Self-Distillation](https://mlsanity.com/paper/2610.14001/) (2026)
- [Self-Distillation with Verbal Regularization](https://mlsanity.com/paper/2610.16354/) (2026)

## Abstract (arXiv)

On-policy self-distillation (OPSD) has emerged as a promising paradigm for improving LLM reasoning, where a privileged teacher with access to reference solutions provides token-level supervision on the student's own generated trajectories. However, we find that OPSD consistently fails on long chain-of-thought (long-CoT) reasoning models, yielding at best marginal gains while destabilizing the reflective reasoning capability these models depend on. Through a novel decomposition of the teacher's supervision signal, we identify the root cause: the teacher's supervision is dominated by a reference-induced component that drives rote memorization of reference-specific shortcuts, while the question-conditioned, inference-transferable component is ignored or actively opposed. Based on this diagnosis, we propose a two-step solution. First, we construct a reference-only teacher (the same model conditioned on the reference without the question) to isolate the non-transferable component of the supervision signal; the residual after subtracting this component captures the question-conditioned, inference-transferable correction. Second, we use pointwise mutual information (PMI) as the mechanism to transform this residual into a well-formed PMI target distribution that the student can directly distill from, filtering out the reference-induced shortcut. Experiments on four long-CoT models across two datasets demonstrate consistent improvements over both the base model and standard OPSD, while preserving the models' natural epistemic behavior throughout training.