# Rethinking On-Policy Distillation of Large Language Models II: One Training Example

arXiv: https://arxiv.org/abs/2609.04172 · HTML: https://mlsanity.com/paper/2609.04172/

## Key facts

- Cited by 24 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 52 of its 58 references that are in the map.
- First posted on arXiv 3 Sep 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 52)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (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)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [M3-Embedding: Multi-Linguality, Multi-Functionality, Multi-Granularity Text Embeddings Through Self-Knowledge Distillation](https://mlsanity.com/paper/2402.03216/) (2024)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [WildChat: 1M ChatGPT Interaction Logs in the Wild](https://mlsanity.com/paper/2405.01470/) (2024)
- [GLM-5: from Vibe Coding to Agentic Engineering](https://mlsanity.com/paper/2602.15763/) (2026)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Magpie: Alignment Data Synthesis from Scratch by Prompting Aligned LLMs with Nothing](https://mlsanity.com/paper/2406.08464/) (2024)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [Learning to Reason without External Rewards](https://mlsanity.com/paper/2505.19590/) (2025)
- [APIGen: Automated Pipeline for Generating Verifiable and Diverse Function-Calling Datasets](https://mlsanity.com/paper/2406.18518/) (2024)
- [Generalizing Verifiable Instruction Following](https://mlsanity.com/paper/2507.02833/) (2025)
- [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)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [TACO: Topics in Algorithmic COde generation dataset](https://mlsanity.com/paper/2312.14852/) (2023)

## Built on by (most cited first, 24 of 24)

- [What Matters in On-Policy Distillation? A Perspective on Data Efficiency and Data Selection](https://mlsanity.com/paper/2609.05198/) (2026)
- [LastOPD: Taming Collapse in Latent On-Policy Distillation](https://mlsanity.com/paper/2609.28845/) (2026)
- [Data-Free On-Policy Distillation: How Far Can We Go Without External Data?](https://mlsanity.com/paper/2609.14193/) (2026)
- [Teaching a Moving Student: Rethinking the Curriculum of On-Policy Distillation](https://mlsanity.com/paper/2609.25048/) (2026)
- [Not Every Token Is Worth Distilling: Selective Supervision for Direct-OPD](https://mlsanity.com/paper/2609.29142/) (2026)
- [Train4Merge: A Controlled Single-Teacher Study of RL vs. SFT Teachers for OPD-Based Model Merging](https://mlsanity.com/paper/2609.32303/) (2026)
- [Trapped by Their Own Rollouts: Understanding Aggregation--Rollout Feedback in Federated On-Policy Distillation](https://mlsanity.com/paper/2609.32573/) (2026)
- [Expected Reasoning-Step Return Unifies On-Policy Learning from Rewards and Teachers](https://mlsanity.com/paper/2609.32674/) (2026)
- [Do We Really Need KL Divergence for On-Policy Distillation of Large Language Models?](https://mlsanity.com/paper/2609.33791/) (2026)
- [Beyond Token Alignment: Event Completion for Cross-Tokenizer On-Policy Distillation](https://mlsanity.com/paper/2609.34738/) (2026)
- [Teacher-Student Gaps Are Not Enough: Outcome-Guided On-Policy Distillation for Multi-Turn Autonomous Agents](https://mlsanity.com/paper/2609.35319/) (2026)
- [d-OPD: Future-Aware On-Policy Distillation for Block Diffusion Language Models](https://mlsanity.com/paper/2609.35362/) (2026)
- [An RL View of OPD: Least Square Policy Distillation for Sample-Efficient LLM Reasoning](https://mlsanity.com/paper/2609.35505/) (2026)
- [Beyond Prompt Count: How Data Shapes Transfer in On-Policy Distillation](https://mlsanity.com/paper/2609.37377/) (2026)
- [Latent-MOPD: Latent Multi-Teacher On-Policy Distillation](https://mlsanity.com/paper/2610.02381/) (2026)
- [What Will Post-Training Fix? Per-Problem Gains Are Shared Across Independent RL Runs, and Existing Checkpoints Predict Them Better Than A Priori Signals](https://mlsanity.com/paper/2610.04978/) (2026)
- [Does On-Policy Distillation for Safety Pose Backdoor Risks?](https://mlsanity.com/paper/2610.07654/) (2026)
- [Why On-Policy Distillation Sometimes Fails: Vanishing Learning Signals](https://mlsanity.com/paper/2610.11247/) (2026)
- [When Do We Need On-Policy Distillation? Distilling on Offline Student Rollouts Is Often Better](https://mlsanity.com/paper/2610.11291/) (2026)
- [DIAL-OPD: Learning More from Fewer Tokens in On-Policy Distillation](https://mlsanity.com/paper/2610.11659/) (2026)
- [Collaborative Learning and Reasoning over Model Slices](https://mlsanity.com/paper/2610.12927/) (2026)
- [State-OPD: State-Grounded On-Policy Distillation for Multi-Turn Agents](https://mlsanity.com/paper/2610.13238/) (2026)
- [JustOPD: On-Policy Distillation from Autoregressive to Diffusion Language Models](https://mlsanity.com/paper/2610.17397/) (2026)
- [MedEvo: Medical Reasoning Evolution through Knowledge Navigation](https://mlsanity.com/paper/2610.17690/) (2026)

## Abstract (arXiv)

On-policy distillation (OPD) combines student-generated rollouts with dense token-level supervision from a teacher. Existing work has mainly studied its algorithmic behavior, leaving the role of training data unclear. We examine this role at the data-minimal limit by training on a single query. One-shot OPD keeps improving for hundreds of steps and recovers most of full-data OPD's gain across task domains and model families. We explain this result through the states visited during training and the rate at which the student aligns with the teacher. We measure state coverage, the fraction of the states full-data OPD visits that a query set's rollouts reach. A single query already reaches (71.5%), most of it within the first 100 steps. Adding semantically distinct queries raises coverage and validation accuracy together, until 16 queries reach (98.9%) and match full-data training. Yet alignment slows at a similar pace whether OPD trains on one query or the whole dataset, and even a fixed set of states takes hundreds of steps to absorb. OPD is therefore data-overfed but algorithm-starved. Its rollouts quickly expose broad supervision, while the student absorbs that supervision increasingly slowly. The state-coverage result extends to multi-teacher OPD, where 16 semantically diverse queries per domain match full-data MOPD. As a further stress test, content-light templates and off-domain WildChat queries also approach the real-query baseline. Task content and induced state coverage can therefore come apart. We hope these findings direct future work toward the step efficiency of OPD, and prompt a re-examination of the data and the mechanisms behind its recent successes in frontier post-training.