# Constitutional On-Policy Safe Distillation

arXiv: https://arxiv.org/abs/2606.03089 · HTML: https://mlsanity.com/paper/2606.03089/

## Key facts

- Cited by 1 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 40 of its 48 references that are in the map.
- First posted on arXiv 2 Jun 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 40)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [MM-Vet: Evaluating Large Multimodal Models for Integrated Capabilities](https://mlsanity.com/paper/2308.02490/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [Vision-R1: Incentivizing Reasoning Capability in Multimodal Large Language Models](https://mlsanity.com/paper/2503.06749/) (2025)
- [Safe RLHF: Safe Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2310.12773/) (2023)
- [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)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Larger language models do in-context learning differently](https://mlsanity.com/paper/2303.03846/) (2023)
- [Safety-Tuned LLaMAs: Lessons From Improving the Safety of Large Language Models that Follow Instructions](https://mlsanity.com/paper/2309.07875/) (2023)
- [LMMs-Eval: Reality Check on the Evaluation of Large Multimodal Models](https://mlsanity.com/paper/2407.12772/) (2024)
- [Deliberative Alignment: Reasoning Enables Safer Language Models](https://mlsanity.com/paper/2412.16339/) (2024)
- [Enhancing the Reasoning Ability of Multimodal Large Language Models via Mixed Preference Optimization](https://mlsanity.com/paper/2411.10442/) (2024)
- [Entropy-Aware On-Policy Distillation of Language Models](https://mlsanity.com/paper/2603.07079/) (2026)
- [Safety Fine-Tuning at (Almost) No Cost: A Baseline for Vision Large Language Models](https://mlsanity.com/paper/2402.02207/) (2024)
- [R1-Zero's "Aha Moment" in Visual Reasoning on a 2B Non-SFT Model](https://mlsanity.com/paper/2503.05132/) (2025)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [Safety Tax: Safety Alignment Makes Your Large Reasoning Models Less Reasonable](https://mlsanity.com/paper/2503.00555/) (2025)
- [Why Does Self-Distillation (Sometimes) Degrade the Reasoning Capability of LLMs?](https://mlsanity.com/paper/2603.24472/) (2026)
- [SPA-VL: A Comprehensive Safety Preference Alignment Dataset for Vision Language Model](https://mlsanity.com/paper/2406.12030/) (2024)
- [MM-RLHF: The Next Step Forward in Multimodal LLM Alignment](https://mlsanity.com/paper/2502.10391/) (2025)
- [Scaling Reasoning Efficiently via Relaxed On-Policy Distillation](https://mlsanity.com/paper/2603.11137/) (2026)

## Built on by (most cited first, 1 of 1)

- [Does On-Policy Distillation for Safety Pose Backdoor Risks?](https://mlsanity.com/paper/2610.07654/) (2026)

## Abstract (arXiv)

On-policy self-distillation (OPSD) has emerged as an efficient post-training paradigm by using a teacher conditioned on privileged information to provide dense token-level supervision. Prior work has shown that OPSD can collapse in verifiable reasoning tasks, while safety alignment differs in that it is guided by high-level constitutions rather than explicit target answers. However, pilot studies reveals that safety OPSD nonetheless suffers from severe collapse, where constitutional conditioning contracts the teacher distribution toward short and overly conservative responses and Reverse KL further amplifies this contraction into reduced expressiveness. We formalize this effect as geometric leakage under safety boundaries in a non-orthogonal semantic space, where safety pressure transfers into the expressiveness dimension. Based on this analysis, we propose Constitutional On-Policy Safety Distillation (COPSD), which first calibrates the teacher through a Cross-SFT cold-start and then performs constitution-conditioned on-policy distillation. Experiments across 3 multimodal large language models (MLLMs) on 12 safety and general benchmarks show that COPSD improves both safety and helpfulness over baselines while reducing the safety tax on general reasoning.