# CapField-OPD: Learning Continuous Capability Fields via Joint-Anchored Multi-Teacher On-Policy Distillation for Flow Models

arXiv: https://arxiv.org/abs/2609.34658 · HTML: https://mlsanity.com/paper/2609.34658/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 36 of its 38 references that are in the map.
- First posted on arXiv 28 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 36)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [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)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Qwen-Image Technical Report](https://mlsanity.com/paper/2508.02324/) (2025)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (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)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [Diffusion Model Alignment Using Direct Preference Optimization](https://mlsanity.com/paper/2311.12908/) (2023)
- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [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)
- [DanceGRPO: Unleashing GRPO on Visual Generation](https://mlsanity.com/paper/2505.07818/) (2025)
- [Improving Video Generation with Human Feedback](https://mlsanity.com/paper/2501.13918/) (2025)
- [Z-Image: An Efficient Image Generation Foundation Model with Single-Stream Diffusion Transformer](https://mlsanity.com/paper/2511.22699/) (2025)
- [Using Human Feedback to Fine-tune Diffusion Models without Any Reward Model](https://mlsanity.com/paper/2311.13231/) (2023)
- [DiffusionNFT: Online Diffusion Reinforcement with Forward Process](https://mlsanity.com/paper/2509.16117/) (2025)
- [HPSv3: Towards Wide-Spectrum Human Preference Score](https://mlsanity.com/paper/2508.03789/) (2025)
- [MixGRPO: Unlocking Flow-based GRPO Efficiency with Mixed ODE-SDE](https://mlsanity.com/paper/2507.21802/) (2025)
- [SANA-Sprint: One-Step Diffusion with Continuous-Time Consistency Distillation](https://mlsanity.com/paper/2503.09641/) (2025)
- [Advantage Weighted Matching: Aligning RL with Pretraining in Diffusion Models](https://mlsanity.com/paper/2509.25050/) (2025)
- [Coefficients-Preserving Sampling for Reinforcement Learning with Flow Matching](https://mlsanity.com/paper/2509.05952/) (2025)
- [DiffusionOPD: A Unified Perspective of On-Policy Distillation in Diffusion Models](https://mlsanity.com/paper/2605.15055/) (2026)
- [Flow-OPD: On-Policy Distillation for Flow Matching Models](https://mlsanity.com/paper/2605.08063/) (2026)
- [Fine-Grained GRPO for Precise Preference Alignment in Flow Models](https://mlsanity.com/paper/2510.01982/) (2025)
- [TwinFlow: Realizing One-step Generation on Large Models with Self-adversarial Flows](https://mlsanity.com/paper/2512.05150/) (2025)
- [DanceOPD: On-Policy Generative Field Distillation](https://mlsanity.com/paper/2606.27377/) (2026)
- [PromptRL: Prompt Matters in RL for Flow-Based Image Generation](https://mlsanity.com/paper/2602.01382/) (2026)

## Abstract (arXiv)

Reward-specialized post-training produces strong experts for flow-based generative models, while multi-teacher on-policy distillation (OPD) consolidates their capabilities into a single student. Existing methods, however, route each prompt to a single teacher according to its semantic category, implicitly binding the desired capability to prompt content. This coupling makes capability invocation vulnerable to prompt perturbations and prevents users from explicitly adjusting the strength of the desired capability at inference time. In this work, we introduce CapField-OPD, an OPD framework that integrates multiple teachers into a continuous capability field through explicit capability coordinates. We use teacher models as anchors to construct this field, with the coordinates determining how their outputs are combined. Each capability configuration thus receives a unique supervision target, and capability control no longer depends on prompt semantics. Since the training anchors may not be optimal at inference time, we further profile the learned field on a small calibration set. The coordinate with the highest mean reward serves as the recommended default, while coordinates that are frequently optimal offer a promising candidate set for test-time scaling. Extensive experiments on compositional generation, text rendering, and visual aesthetics demonstrate that CapField-OPD consolidates multiple specialized teachers into a single student while preserving or surpassing their performance, reliably invokes the desired capabilities under semantics-preserving prompt variations, and supports continuous capability control and coordinate-based test-time scaling.