# DreOPD: Degraded-Reference Extrapolative On-Policy Distillation for Flow-matching Models

arXiv: https://arxiv.org/abs/2608.09233 · HTML: https://mlsanity.com/paper/2608.09233/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 37 of its 39 references that are in the map.
- First posted on arXiv 10 Aug 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- 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 37)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [GenEval: An Object-Focused Framework for Evaluating Text-to-Image Alignment](https://mlsanity.com/paper/2310.11513/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Diffusion Model Alignment Using Direct Preference Optimization](https://mlsanity.com/paper/2311.12908/) (2023)
- [Flow-GRPO: Training Flow Matching Models via Online RL](https://mlsanity.com/paper/2505.05470/) (2025)
- [DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Models](https://mlsanity.com/paper/2305.16381/) (2023)
- [Directly Fine-Tuning Diffusion Models on Differentiable Rewards](https://mlsanity.com/paper/2309.17400/) (2023)
- [DanceGRPO: Unleashing GRPO on Visual Generation](https://mlsanity.com/paper/2505.07818/) (2025)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Aligning Text-to-Image Diffusion Models with Reward Backpropagation](https://mlsanity.com/paper/2310.03739/) (2023)
- [Human Preference Score: Better Aligning Text-to-Image Models with Human Preference](https://mlsanity.com/paper/2303.14420/) (2023)
- [DiffusionNFT: Online Diffusion Reinforcement with Forward Process](https://mlsanity.com/paper/2509.16117/) (2025)
- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)
- [MixGRPO: Unlocking Flow-based GRPO Efficiency with Mixed ODE-SDE](https://mlsanity.com/paper/2507.21802/) (2025)
- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [Controllable Generation with Text-to-Image Diffusion Models: A Survey](https://mlsanity.com/paper/2403.04279/) (2024)
- [Vision-OPD: Learning to See Fine Details for Multimodal LLMs via On-Policy Self-Distillation](https://mlsanity.com/paper/2605.18740/) (2026)
- [Advantage Weighted Matching: Aligning RL with Pretraining in Diffusion Models](https://mlsanity.com/paper/2509.25050/) (2025)
- [GRPO-Guard: Mitigating Implicit Over-Optimization in Flow Matching via Regulated Clipping](https://mlsanity.com/paper/2510.22319/) (2025)
- [DiffusionOPD: A Unified Perspective of On-Policy Distillation in Diffusion Models](https://mlsanity.com/paper/2605.15055/) (2026)

## Built on by (most cited first, 2 of 2)

- [CapField-OPD: Learning Continuous Capability Fields via Joint-Anchored Multi-Teacher On-Policy Distillation for Flow Models](https://mlsanity.com/paper/2609.34658/) (2026)
- [PE-OPSD: Internalizing Prompt Enhancement into Flow-matching Models via On-Policy Self-Distillation](https://mlsanity.com/paper/2609.36638/) (2026)

## Abstract (arXiv)

Flow-matching models are now a mainstream method to image generation, but its adaptation to diverse downstream scenarios typically relies on post-training, which may cause conflicts among task-specific optimization objectives. Reinforcement learning enables direct optimization of task-specific rewards beyond the original models, yet trajectory-level optimization may incur high-variance gradients and cross-task interference. On-policy distillation (OPD) offers dense and stable supervision on student rollouts, but conventional teacher matching remains imitation-based. We propose DreOPD, a Degraded-reference extrapolative OPD method for flow-matching models that bridges these two paradigms. Our DreOPD converts implicit reward extrapolation into closed-form velocity regression, enabling extrapolative post-training with the stability of OPD. It further uses a mildly degraded reference to strengthen the teacher-reference contrast, yielding a clearer extrapolation direction. Experiments on single- and multi-teacher settings show that DreOPD outperforms OPD and multi-task RL baselines in average performance, while surpassing specialized teachers on most metrics.