# Euphonium: Steering Video Flow Matching via Process Reward Gradient Guided Stochastic Dynamics

arXiv: https://arxiv.org/abs/2602.04928 · HTML: https://mlsanity.com/paper/2602.04928/

## 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 30 of its 36 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- LLM alignment / RLHF / preference optimisation / [Diffusion and multimodal model alignment](https://mlsanity.com/alignment/diffusion-and-multimodal-model-alignment/)

## Builds on (most cited first, 30 of 30)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [InternVL3: Exploring Advanced Training and Test-Time Recipes for Open-Source Multimodal Models](https://mlsanity.com/paper/2504.10479/) (2025)
- [HunyuanVideo: A Systematic Framework For Large Video Generative Models](https://mlsanity.com/paper/2412.03603/) (2024)
- [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)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Flow-GRPO: Training Flow Matching Models via Online RL](https://mlsanity.com/paper/2505.05470/) (2025)
- [PyTorch FSDP: Experiences on Scaling Fully Sharded Data Parallel](https://mlsanity.com/paper/2304.11277/) (2023)
- [DanceGRPO: Unleashing GRPO on Visual Generation](https://mlsanity.com/paper/2505.07818/) (2025)
- [VBench-2.0: Advancing Video Generation Benchmark Suite for Intrinsic Faithfulness](https://mlsanity.com/paper/2503.21755/) (2025)
- [Improving Video Generation with Human Feedback](https://mlsanity.com/paper/2501.13918/) (2025)
- [Seedance 1.0: Exploring the Boundaries of Video Generation Models](https://mlsanity.com/paper/2506.09113/) (2025)
- [MixGRPO: Unlocking Flow-based GRPO Efficiency with Mixed ODE-SDE](https://mlsanity.com/paper/2507.21802/) (2025)
- [Guided Flows for Generative Modeling and Decision Making](https://mlsanity.com/paper/2311.13443/) (2023)
- [TempFlow-GRPO: When Timing Matters for GRPO in Flow Models](https://mlsanity.com/paper/2508.04324/) (2025)
- [NETS: A Non-Equilibrium Transport Sampler](https://mlsanity.com/paper/2410.02711/) (2024)
- [Video-T1: Test-Time Scaling for Video Generation](https://mlsanity.com/paper/2503.18942/) (2025)
- [TreeGRPO: Tree-Advantage GRPO for Online RL Post-Training of Diffusion Models](https://mlsanity.com/paper/2512.08153/) (2025)
- [Video Generation Models Are Good Latent Reward Models](https://mlsanity.com/paper/2511.21541/) (2025)
- [Principled RL for Flow Matching Emerges from the Chunk-level Policy Optimization](https://mlsanity.com/paper/2510.21583/) (2025)
- [Value Gradient Guidance for Flow Matching Alignment](https://mlsanity.com/paper/2512.05116/) (2025)
- [E-GRPO: High Entropy Steps Drive Effective Reinforcement Learning for Flow Models](https://mlsanity.com/paper/2601.00423/) (2026)

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

- [Advances in GRPO for Generation Models: A Survey](https://mlsanity.com/paper/2603.06623/) (2026)
- [Video Generation Models: A Survey of Post-Training and Alignment](https://mlsanity.com/paper/2610.00812/) (2026)

## Abstract (arXiv)

While online Reinforcement Learning has emerged as a crucial technique for aligning flow matching models with human preferences, current approaches are hindered by inefficient exploration during training rollouts. Relying on undirected stochasticity and sparse outcome rewards, these methods struggle to discover high-reward samples, resulting in data-inefficient and slow optimization. To address these limitations, we propose Euphonium, a novel framework that steers generation via process reward gradient guided dynamics. Our key insight is to formulate the sampling process as a theoretically principled Stochastic Differential Equation that explicitly incorporates the gradient of a Process Reward Model into the flow drift. This design enables dense, step-by-step steering toward high-reward regions, advancing beyond the unguided exploration in prior works, and theoretically encompasses existing sampling methods (e.g., Flow-GRPO, DanceGRPO) as special cases. We further derive a distillation objective that internalizes the guidance signal into the flow network, eliminating inference-time dependency on the reward model. We instantiate this framework with a Dual-Reward Group Relative Policy Optimization algorithm, combining latent process rewards for efficient credit assignment with pixel-level outcome rewards for final visual fidelity. Experiments on text-to-video generation show that Euphonium achieves better alignment compared to existing methods while accelerating training convergence by 1.66x. Our code is available at https://github.com/zerzerzerz/Euphonium