# Energy-Weighted Flow Matching for Offline Reinforcement Learning

arXiv: https://arxiv.org/abs/2503.04975 · HTML: https://mlsanity.com/paper/2503.04975/

## Key facts

- Cited by 73 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 35 of its 38 references that are in the map.
- First posted on arXiv 6 Mar 2025.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- Offline RL and imitation learning from data / [Diffusion and flow policies for offline RL](https://mlsanity.com/offlinerl/diffusion-and-flow-policies-for-offline-rl/)

## Builds on (most cited first, 30 of 35)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [IDQL: Implicit Q-Learning as an Actor-Critic Method with Diffusion Policies](https://mlsanity.com/paper/2304.10573/) (2023)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [Offline Reinforcement Learning via High-Fidelity Generative Behavior Modeling](https://mlsanity.com/paper/2209.14548/) (2022)
- [Efficient Diffusion Policies for Offline Reinforcement Learning](https://mlsanity.com/paper/2305.20081/) (2023)
- [Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learning](https://mlsanity.com/paper/2304.12824/) (2023)
- [Diffusion-based Reinforcement Learning via Q-weighted Variational Policy Optimization](https://mlsanity.com/paper/2405.16173/) (2024)
- [Synthetic Experience Replay](https://mlsanity.com/paper/2303.06614/) (2023)
- [Guided Flows for Generative Modeling and Decision Making](https://mlsanity.com/paper/2311.13443/) (2023)
- [Score Regularized Policy Optimization through Diffusion Behavior](https://mlsanity.com/paper/2310.07297/) (2023)
- [Improved off-policy training of diffusion samplers](https://mlsanity.com/paper/2402.05098/) (2024)
- [Protein Conformation Generation via Force-Guided SE(3) Diffusion Models](https://mlsanity.com/paper/2403.14088/) (2024)

## Built on by (most cited first, 30 of 73)

- [Steering Your Diffusion Policy with Latent Space Reinforcement Learning](https://mlsanity.com/paper/2506.15799/) (2025)
- [wd1: Weighted Policy Optimization for Reasoning in Diffusion Language Models](https://mlsanity.com/paper/2507.08838/) (2025)
- [A Vision-Language-Action-Critic Model for Robotic Real-World Reinforcement Learning](https://mlsanity.com/paper/2509.15937/) (2025)
- [Flow-Based Policy for Online Reinforcement Learning](https://mlsanity.com/paper/2506.12811/) (2025)
- [Q-learning with Adjoint Matching](https://mlsanity.com/paper/2601.14234/) (2026)
- [EXPO: Stable Reinforcement Learning with Expressive Policies](https://mlsanity.com/paper/2507.07986/) (2025)
- [Scaling Offline RL via Efficient and Expressive Shortcut Models](https://mlsanity.com/paper/2505.22866/) (2025)
- [One-Step Flow Policy Mirror Descent](https://mlsanity.com/paper/2507.23675/) (2025)
- [Flow Policy Gradients for Robot Control](https://mlsanity.com/paper/2602.02481/) (2026)
- [FlowQ: Energy-Guided Flow Policies for Offline Reinforcement Learning](https://mlsanity.com/paper/2505.14139/) (2025)
- [Learning While Deploying: Fleet-Scale Reinforcement Learning for Generalist Robot Policies](https://mlsanity.com/paper/2605.00416/) (2026)
- [Multi-agent Coordination via Flow Matching](https://mlsanity.com/paper/2511.05005/) (2025)
- [Guided Flow Policy: Learning from High-Value Actions in Offline Reinforcement Learning](https://mlsanity.com/paper/2512.03973/) (2025)
- [OM2P: Offline Multi-Agent Mean-Flow Policy](https://mlsanity.com/paper/2508.06269/) (2025)
- [Unleashing Flow Policies with Distributional Critics](https://mlsanity.com/paper/2509.23087/) (2025)
- [Energy-Weighted Flow Matching: Unlocking Continuous Normalizing Flows for Efficient and Scalable Boltzmann Sampling](https://mlsanity.com/paper/2509.03726/) (2025)
- [Diffusion LLMs are Natural Adversaries for any LLM](https://mlsanity.com/paper/2511.00203/) (2025)
- [Discrete Guidance Matching: Exact Guidance for Discrete Flow Matching](https://mlsanity.com/paper/2509.21912/) (2025)
- [Expressive Value Learning for Scalable Offline Reinforcement Learning](https://mlsanity.com/paper/2510.08218/) (2025)
- [Flow Actor-Critic for Offline Reinforcement Learning](https://mlsanity.com/paper/2602.18015/) (2026)
- [Q-Flow: Stable and Expressive Reinforcement Learning with Flow-Based Policy](https://mlsanity.com/paper/2605.13435/) (2026)
- [GDSD: Reinforcement Learning as Guided Denoiser Self-Distillation for Diffusion Language Models](https://mlsanity.com/paper/2605.29398/) (2026)
- [Test-Time Gradient Guidance of Flow Policies in Reinforcement Learning](https://mlsanity.com/paper/2606.11087/) (2026)
- [FlowAWR: Online Adaptive Flow Reinforcement via Advantage-Weighted Rectification](https://mlsanity.com/paper/2606.30376/) (2026)
- [DeFlow: Decoupling Manifold Modeling and Value Maximization for Offline Policy Extraction](https://mlsanity.com/paper/2601.10471/) (2026)
- [PolicyFlow: Policy Optimization with Continuous Normalizing Flow in Reinforcement Learning](https://mlsanity.com/paper/2602.01156/) (2026)
- [Scalable Maximum Entropy Reinforcement Learning for Diffusion Policies via Adjoint Matching](https://mlsanity.com/paper/2606.22630/) (2026)
- [Weighted Conditional Flow Matching](https://mlsanity.com/paper/2507.22270/) (2025)
- [ReFORM: Reflected Flows for On-support Offline RL via Noise Manipulation](https://mlsanity.com/paper/2602.05051/) (2026)
- [Safe Flow Q-Learning: Offline Safe Reinforcement Learning with Reachability-Based Flow Policies](https://mlsanity.com/paper/2603.15136/) (2026)

## Abstract (arXiv)

This paper investigates energy guidance in generative modeling, where the target distribution is defined as q(mathbf x) propto p(mathbf x)exp(-β mathcal E(mathbf x)), with p(mathbf x) being the data distribution and mathcal E(mathcal x) as the energy function. To comply with energy guidance, existing methods often require auxiliary procedures to learn intermediate guidance during the diffusion process. To overcome this limitation, we explore energy-guided flow matching, a generalized form of the diffusion process. We introduce energy-weighted flow matching (EFM), a method that directly learns the energy-guided flow without the need for auxiliary models. Theoretical analysis shows that energy-weighted flow matching accurately captures the guided flow. Additionally, we extend this methodology to energy-weighted diffusion models and apply it to offline reinforcement learning (RL) by proposing the Q-weighted Iterative Policy Optimization (QIPO). Empirically, we demonstrate that the proposed QIPO algorithm improves performance in offline RL tasks. Notably, our algorithm is the first energy-guided diffusion model that operates independently of auxiliary models and the first exact energy-guided flow matching model in the literature.