# Demystifying OPD: Length Inflation and Stabilization Strategies for Large Language Models

arXiv: https://arxiv.org/abs/2604.08527 · HTML: https://mlsanity.com/paper/2604.08527/

## Key facts

- Cited by 30 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 28 of its 30 references that are in the map.
- First posted on arXiv 9 Apr 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, 28 of 28)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Policy Distillation](https://mlsanity.com/paper/1511.06295/) (2015)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [MiMo-V2-Flash Technical Report](https://mlsanity.com/paper/2601.02780/) (2026)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [Why Does Self-Distillation (Sometimes) Degrade the Reasoning Capability of LLMs?](https://mlsanity.com/paper/2603.24472/) (2026)
- [Distilling Policy Distillation](https://mlsanity.com/paper/1902.02186/) (2019)
- [Black-Box On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2511.10643/) (2025)
- [Dual Policy Distillation](https://mlsanity.com/paper/2006.04061/) (2020)

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

- [Uni-OPD: Unifying On-Policy Distillation with a Dual-Perspective Recipe](https://mlsanity.com/paper/2605.03677/) (2026)
- [The Many Faces of On-Policy Distillation: Pitfalls, Mechanisms, and Fixes](https://mlsanity.com/paper/2605.11182/) (2026)
- [Filter, Then Reweight: Rethinking Optimization Granularity in On-Policy Distillation](https://mlsanity.com/paper/2606.02684/) (2026)
- [Decoupling KL and Trajectories: A Unified Perspective for SFT, DAgger, Offline RL, and OPD in LLM Distillation](https://mlsanity.com/paper/2605.16826/) (2026)
- [Trajectory-Refined Distillation](https://mlsanity.com/paper/2606.08432/) (2026)
- [SAGE-OPD: Selective Agent-Guided Intervention for Multi-Turn On-Policy Distillation](https://mlsanity.com/paper/2606.19659/) (2026)
- [DanceOPD: On-Policy Generative Field Distillation](https://mlsanity.com/paper/2606.27377/) (2026)
- [ViCuR: Visual Cues as Recoverable Privilege for Multimodal On-Policy Distillation](https://mlsanity.com/paper/2606.05718/) (2026)
- [Mismatch Matters: On-Policy Distillation Beyond Token Agreement](https://mlsanity.com/paper/2608.09836/) (2026)
- [UniSD: Towards a Unified Self-Distillation Framework for Large Language Models](https://mlsanity.com/paper/2605.06597/) (2026)
- [OmniOPD: Logit-Free On-Policy Distillation via Speculative Verification](https://mlsanity.com/paper/2606.01476/) (2026)
- [SAF-OPD: Stable Advantage Fusion for On-Policy Distillation](https://mlsanity.com/paper/2607.29209/) (2026)
- [When EOS Tokens Disagree: Understanding Length Inflation in On-Policy Distillation](https://mlsanity.com/paper/2609.20511/) (2026)
- [Privileged Likelihood Is Not Automatically Value: Three Checks for Token Credit in On-Policy Self-Distillation](https://mlsanity.com/paper/2608.09263/) (2026)
- [Every Coin Has Two Sides: On the Dual Nature of Generalization in On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2608.16647/) (2026)
- [SEER: Long-Context Reasoning via Selective Visual-Text Compression](https://mlsanity.com/paper/2608.15962/) (2026)
- [Learning at the Right Pace: Adaptive Data Scheduling Improves LLM Reinforcement Learning](https://mlsanity.com/paper/2606.22305/) (2026)
- [What Should a Self-Teacher See? Privileged Context Design for On-Policy Self-Distillation](https://mlsanity.com/paper/2609.25623/) (2026)
- [Understanding On-Policy Distillation: A Mechanistic Interpretability Perspective via Sparse Crosscoders](https://mlsanity.com/paper/2609.35210/) (2026)
- [Blockwise Policy-Drift Gating for On-Policy Distillation](https://mlsanity.com/paper/2606.24084/) (2026)
- [SR-OPSD: Self-Referenced On-Policy Self-Distillation](https://mlsanity.com/paper/2608.09745/) (2026)
- [Tool-Augmented On-Policy Distillation for LLM Domain Adaptation in Sequence-Based Omics Tasks](https://mlsanity.com/paper/2609.23435/) (2026)
- [Understanding Off- vs On-Policy Distillation: A Tale of Distinct Training Objectives](https://mlsanity.com/paper/2609.38666/) (2026)
- [Diagnosing On-Policy Self-Distillation for Reasoning Language Models](https://mlsanity.com/paper/2609.39118/) (2026)
- [Learning to Revise Reasoning with Segment-wise On-Policy Distillation](https://mlsanity.com/paper/2610.02703/) (2026)
- [Gains and Collapse in On-Policy Distillation:A Reinforcement Learning Perspective](https://mlsanity.com/paper/2610.03185/) (2026)
- [When Do We Need On-Policy Distillation? Distilling on Offline Student Rollouts Is Often Better](https://mlsanity.com/paper/2610.11291/) (2026)
- [Branching On-Policy Distillation](https://mlsanity.com/paper/2610.13481/) (2026)
- [Token Utility for On-Policy Distillation via Local Trust-Region Optimization](https://mlsanity.com/paper/2610.18883/) (2026)
- [DTDD: Divergence-Triggered Dynamic Distillation for Reliable On-Policy Supervision](https://mlsanity.com/paper/2610.19302/) (2026)

## Abstract (arXiv)

On-policy distillation (OPD) trains student models under their own induced distribution while leveraging supervision from stronger teachers. We identify a failure mode of OPD: as training progresses, on-policy rollouts can undergo abrupt length inflation, causing truncated trajectories to dominate the training data. This truncation collapse coincides with abrupt repetition saturation and induces biased gradient signals, leading to severe training instability and sharp degradation in validation performance. We attribute this problem to the interaction between student-induced data collection and the distillation objective, which implicitly favors long and repetitive rollouts. To address this issue, we propose StableOPD, a stabilized OPD framework that combines a reference-based divergence constraint with rollout mixture distillation. These together mitigate repetition-induced length inflation and further stabilize OPD training. Across multiple math reasoning datasets, our approach prevents truncation collapse, stabilizes training dynamics, and improves performance by 7.2% on average.