# Scores as Actions: a framework of fine-tuning diffusion models by continuous-time reinforcement learning

arXiv: https://arxiv.org/abs/2409.08400 · HTML: https://mlsanity.com/paper/2409.08400/

## Key facts

- Cited by 19 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 38 of its 58 references that are in the map.
- First posted on arXiv 12 Sep 2024.

## 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 38)

- [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)
- [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)
- [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)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [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)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [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)
- [DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Models](https://mlsanity.com/paper/2305.16381/) (2023)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Aligning Text-to-Image Models using Human Feedback](https://mlsanity.com/paper/2302.12192/) (2023)
- [Training-Free Structured Diffusion Guidance for Compositional Text-to-Image Synthesis](https://mlsanity.com/paper/2212.05032/) (2022)
- [Stable Bias: Analyzing Societal Representations in Diffusion Models](https://mlsanity.com/paper/2303.11408/) (2023)
- [Optimizing Prompts for Text-to-Image Generation](https://mlsanity.com/paper/2212.09611/) (2022)
- [A Variational Perspective on Diffusion-Based Generative Models and Score Matching](https://mlsanity.com/paper/2106.02808/) (2021)
- [Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Control](https://mlsanity.com/paper/2402.15194/) (2024)
- [gDDIM: Generalized denoising diffusion implicit models](https://mlsanity.com/paper/2206.05564/) (2022)
- [Policy Gradient and Actor-Critic Learning in Continuous Time and Space: Theory and Algorithms](https://mlsanity.com/paper/2111.11232/) (2021)
- [Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Review](https://mlsanity.com/paper/2407.13734/) (2024)
- [Benchmarking Spatial Relationships in Text-to-Image Generation](https://mlsanity.com/paper/2212.10015/) (2022)

## Built on by (most cited first, 19 of 19)

- [Score as Action: Fine-Tuning Diffusion Generative Models by Continuous-time Reinforcement Learning](https://mlsanity.com/paper/2502.01819/) (2025)
- [RePrompt: Reasoning-Augmented Reprompting for Text-to-Image Generation via Reinforcement Learning](https://mlsanity.com/paper/2505.17540/) (2025)
- [Stochastic Control for Fine-tuning Diffusion Models: Optimality, Regularity, and Convergence](https://mlsanity.com/paper/2412.18164/) (2024)
- [Flow Density Control: Generative Optimization Beyond Entropy-Regularized Fine-Tuning](https://mlsanity.com/paper/2511.22640/) (2025)
- [Provable Maximum Entropy Manifold Exploration via Diffusion Models](https://mlsanity.com/paper/2506.15385/) (2025)
- [Regret of exploratory policy improvement and q-learning](https://mlsanity.com/paper/2411.01302/) (2024)
- [Conditional Diffusion Guidance under Hard Constraint: A Stochastic Analysis Approach](https://mlsanity.com/paper/2602.05533/) (2026)
- [Composition and Alignment of Diffusion Models using Constrained Learning](https://mlsanity.com/paper/2508.19104/) (2025)
- [Towards a unified framework for guided diffusion models](https://mlsanity.com/paper/2512.04985/) (2025)
- [Understanding Sampler Stochasticity in Training Diffusion Models for RLHF](https://mlsanity.com/paper/2510.10767/) (2025)
- [Verifier-Constrained Flow Expansion for Discovery Beyond the Data](https://mlsanity.com/paper/2602.15984/) (2026)
- [Direct Distributional Optimization for Provable Alignment of Diffusion Models](https://mlsanity.com/paper/2502.02954/) (2025)
- [Improved techniques for fine-tuning flow models via adjoint matching: a deterministic control pipeline](https://mlsanity.com/paper/2605.06583/) (2026)
- [ART for Diffusion Sampling: A Reinforcement Learning Approach to Timestep Schedule](https://mlsanity.com/paper/2601.18681/) (2026)
- [A Unified Density Operator View of Flow Control and Merging](https://mlsanity.com/paper/2602.08012/) (2026)
- [A Continuous-Time Reinforcement Learning Framework for Fine-Tuning Discrete Diffusion Models](https://mlsanity.com/paper/2607.14522/) (2026)
- [DOHF: Online Diffusion Fine-tuning with Doob's h-transform Guidance](https://mlsanity.com/paper/2609.31882/) (2026)
- [Rethinking Floorplan Generation with Space Syntax: From Design Theory to Model Improvement](https://mlsanity.com/paper/2602.22507/) (2026)
- [ART for Diffusion Sampling: Continuous-Time Control and Actor-Critic Learning](https://mlsanity.com/paper/2607.02137/) (2026)

## Abstract (arXiv)

Reinforcement Learning from human feedback (RLHF) has been shown a promising direction for aligning generative models with human intent and has also been explored in recent works for alignment of diffusion generative models. In this work, we provide a rigorous treatment by formulating the task of fine-tuning diffusion models, with reward functions learned from human feedback, as an exploratory continuous-time stochastic control problem. Our key idea lies in treating the score-matching functions as controls/actions, and upon this, we develop a unified framework from a continuous-time perspective, to employ reinforcement learning (RL) algorithms in terms of improving the generation quality of diffusion models. We also develop the corresponding continuous-time RL theory for policy optimization and regularization under assumptions of stochastic different equations driven environment. Experiments on the text-to-image (T2I) generation will be reported in the accompanied paper.