# Score as Action: Fine-Tuning Diffusion Generative Models by Continuous-time Reinforcement Learning

arXiv: https://arxiv.org/abs/2502.01819 · HTML: https://mlsanity.com/paper/2502.01819/

## Key facts

- Cited by 33 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 54 of its 65 references that are in the map.
- First posted on arXiv 3 Feb 2025.

## 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/)
- Deep reinforcement learning methods / [RL with diffusion and flow models](https://mlsanity.com/deeprl/rl-with-diffusion-and-flow-models/)

## Builds on (most cited first, 30 of 54)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [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)
- [Diffusion Model Alignment Using Direct Preference Optimization](https://mlsanity.com/paper/2311.12908/) (2023)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Models](https://mlsanity.com/paper/2305.16381/) (2023)

## Built on by (most cited first, 30 of 33)

- [Flow-GRPO: Training Flow Matching Models via Online RL](https://mlsanity.com/paper/2505.05470/) (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)
- [Reinforce Adjoint Matching: Scaling RL Post-Training of Diffusion and Flow-Matching Models](https://mlsanity.com/paper/2605.10759/) (2026)
- [Taming Preference Mode Collapse via Directional Decoupling Alignment in Diffusion Reinforcement Learning](https://mlsanity.com/paper/2512.24146/) (2025)
- [UniGRPO: Unified Policy Optimization for Reasoning-Driven Visual Generation](https://mlsanity.com/paper/2603.23500/) (2026)
- [The Image as Its Own Reward: Reinforcement Learning with Adversarial Reward for Image Generation](https://mlsanity.com/paper/2511.20256/) (2025)
- [HardFlow: Hard-Constrained Sampling for Flow-Matching Models via Trajectory Optimization](https://mlsanity.com/paper/2511.08425/) (2025)
- [Conditional Diffusion Guidance under Hard Constraint: A Stochastic Analysis Approach](https://mlsanity.com/paper/2602.05533/) (2026)
- [Identity-GRPO: Optimizing Multi-Human Identity-preserving Video Generation via Reinforcement Learning](https://mlsanity.com/paper/2510.14256/) (2025)
- [Understanding Sampler Stochasticity in Training Diffusion Models for RLHF](https://mlsanity.com/paper/2510.10767/) (2025)
- [PaCo-RL: Advancing Reinforcement Learning for Consistent Image Generation with Pairwise Reward Modeling](https://mlsanity.com/paper/2512.04784/) (2025)
- [Reward Score Matching: Unifying Reward-based Fine-tuning for Flow and Diffusion Models](https://mlsanity.com/paper/2604.17415/) (2026)
- [Improved techniques for fine-tuning flow models via adjoint matching: a deterministic control pipeline](https://mlsanity.com/paper/2605.06583/) (2026)
- [Embedding-perturbed Exploration Preference Optimization for Flow Models](https://mlsanity.com/paper/2605.15803/) (2026)
- [MultiCrafter: High-Fidelity Multi-Subject Generation via Disentangled Attention and Identity-Aware Preference Alignment](https://mlsanity.com/paper/2509.21953/) (2025)
- [Continuous Q-Score Matching: Diffusion Guided Reinforcement Learning for Continuous-Time Control](https://mlsanity.com/paper/2510.17122/) (2025)
- [ART for Diffusion Sampling: A Reinforcement Learning Approach to Timestep Schedule](https://mlsanity.com/paper/2601.18681/) (2026)
- [Efficient Adjoint Matching for Fine-tuning Diffusion Models](https://mlsanity.com/paper/2605.11480/) (2026)
- [Is RL fine-tuning harder than regression? A PDE learning approach for diffusion models](https://mlsanity.com/paper/2509.02528/) (2025)
- [Diffusion Generative Models Meet Compressed Sensing, with Applications to Imaging and Finance](https://mlsanity.com/paper/2509.03898/) (2025)
- [Parallel Diffusion Solver via Residual Dirichlet Policy Optimization](https://mlsanity.com/paper/2512.22796/) (2025)
- [Constrained Flow Optimization via Sequential Fine Tuning for Molecular Design](https://mlsanity.com/paper/2605.30610/) (2026)
- [What Happens Next? Next Scene Prediction with a Unified Video Model](https://mlsanity.com/paper/2512.13015/) (2025)
- [Improving Text-to-Image Generation with Intrinsic Self-Confidence Rewards](https://mlsanity.com/paper/2603.00918/) (2026)
- [A Continuous-Time Reinforcement Learning Framework for Fine-Tuning Discrete Diffusion Models](https://mlsanity.com/paper/2607.14522/) (2026)
- [Amortized Guidance for Image Inpainting with Pretrained Diffusion Models](https://mlsanity.com/paper/2605.13010/) (2026)
- [DriveAnchor: Progressive Anchor-based Flow Learning for Autonomous Driving Planning](https://mlsanity.com/paper/2606.00519/) (2026)
- [DOHF: Online Diffusion Fine-tuning with Doob's h-transform Guidance](https://mlsanity.com/paper/2609.31882/) (2026)
- [Explicit Critic Guidance for Aligning Diffusion Models](https://mlsanity.com/paper/2605.27736/) (2026)

## Abstract (arXiv)

Reinforcement learning from human feedback (RLHF), which aligns a diffusion model with input prompt, has become a crucial step in building reliable generative AI models. Most works in this area use a discrete-time formulation, which is prone to induced discretization errors, and often not applicable to models with higher-order/black-box solvers. The objective of this study is to develop a disciplined approach to fine-tune diffusion models using continuous-time RL, formulated as a stochastic control problem with a reward function that aligns the end result (terminal state) with input prompt. The key idea is to treat score matching as controls or actions, and thereby making connections to policy optimization and regularization in continuous-time RL. To carry out this idea, we lay out a new policy optimization framework for continuous-time RL, and illustrate its potential in enhancing the value networks design space via leveraging the structural property of diffusion models. We validate the advantages of our method by experiments in downstream tasks of fine-tuning large-scale Text2Image models of Stable Diffusion v1.5.