# Flow Q-Learning

arXiv: https://arxiv.org/abs/2502.02538 · HTML: https://mlsanity.com/paper/2502.02538/

## Key facts

- Cited by 184 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 79 of its 95 references that are in the map.
- First posted on arXiv 4 Feb 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/)
- 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 79)

- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [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)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [A Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06860/) (2021)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [Open X-Embodiment: Robotic Learning Datasets and RT-X Models](https://mlsanity.com/paper/2310.08864/) (2023)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [What Matters in Learning from Offline Human Demonstrations for Robot Manipulation](https://mlsanity.com/paper/2108.03298/) (2021)
- [AWAC: Accelerating Online Reinforcement Learning with Offline Datasets](https://mlsanity.com/paper/2006.09359/) (2020)
- [Behavior Regularized Offline Reinforcement Learning](https://mlsanity.com/paper/1911.11361/) (2019)
- [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)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Efficient Online Reinforcement Learning with Offline Data](https://mlsanity.com/paper/2302.02948/) (2023)

## Built on by (most cited first, 30 of 184)

- [Steering Your Diffusion Policy with Latent Space Reinforcement Learning](https://mlsanity.com/paper/2506.15799/) (2025)
- [Reinforcement Learning with Action Chunking](https://mlsanity.com/paper/2507.07969/) (2025)
- [A Vision-Language-Action-Critic Model for Robotic Real-World Reinforcement Learning](https://mlsanity.com/paper/2509.15937/) (2025)
- [RL-100: Performant Robotic Manipulation with Real-World Reinforcement Learning](https://mlsanity.com/paper/2510.14830/) (2025)
- [Diffusion Guidance Is a Controllable Policy Improvement Operator](https://mlsanity.com/paper/2505.23458/) (2025)
- [Horizon Reduction Makes RL Scalable](https://mlsanity.com/paper/2506.04168/) (2025)
- [RL Token: Bootstrapping Online RL with Vision-Language-Action Models](https://mlsanity.com/paper/2604.23073/) (2026)
- [FlowRL: Matching Reward Distributions for LLM Reasoning](https://mlsanity.com/paper/2509.15207/) (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)
- [SAC Flow: Sample-Efficient Reinforcement Learning of Flow-Based Policies via Velocity-Reparameterized Sequential Modeling](https://mlsanity.com/paper/2509.25756/) (2025)
- [Scaling Offline RL via Efficient and Expressive Shortcut Models](https://mlsanity.com/paper/2505.22866/) (2025)
- [Bigger, Regularized, Categorical: High-Capacity Value Functions are Efficient Multi-Task Learners](https://mlsanity.com/paper/2505.23150/) (2025)
- [floq: Training Critics via Flow-Matching for Scaling Compute in Value-Based RL](https://mlsanity.com/paper/2509.06863/) (2025)
- [TD-JEPA: Latent-predictive Representations for Zero-Shot Reinforcement Learning](https://mlsanity.com/paper/2510.00739/) (2025)
- [One-Step Flow Policy Mirror Descent](https://mlsanity.com/paper/2507.23675/) (2025)
- [GenPO: Generative Diffusion Models Meet On-Policy Reinforcement Learning](https://mlsanity.com/paper/2505.18763/) (2025)
- [Dual Goal Representations](https://mlsanity.com/paper/2510.06714/) (2025)
- [Flow Policy Gradients for Robot Control](https://mlsanity.com/paper/2602.02481/) (2026)
- [Value Flows](https://mlsanity.com/paper/2510.07650/) (2025)
- [Learning While Deploying: Fleet-Scale Reinforcement Learning for Generalist Robot Policies](https://mlsanity.com/paper/2605.00416/) (2026)
- [Prior-Guided Diffusion Planning for Offline Reinforcement Learning](https://mlsanity.com/paper/2505.10881/) (2025)
- [Normalizing Flows are Capable Models for Continuous Control](https://mlsanity.com/paper/2505.23527/) (2025)
- [Flow-Based Single-Step Completion for Efficient and Expressive Policy Learning](https://mlsanity.com/paper/2506.21427/) (2025)
- [Scalable Offline Model-Based RL with Action Chunks](https://mlsanity.com/paper/2512.08108/) (2025)
- [Graph-Assisted Stitching for Offline Hierarchical Reinforcement Learning](https://mlsanity.com/paper/2506.07744/) (2025)
- [Simplicial Embeddings Improve Sample Efficiency in Actor-Critic Agents](https://mlsanity.com/paper/2510.13704/) (2025)
- [Transitive RL: Value Learning via Divide and Conquer](https://mlsanity.com/paper/2510.22512/) (2025)
- [Reverse Flow Matching: A Unified Framework for Online Reinforcement Learning with Diffusion and Flow Policies](https://mlsanity.com/paper/2601.08136/) (2026)

## Abstract (arXiv)

We present flow Q-learning (FQL), a simple and performant offline reinforcement learning (RL) method that leverages an expressive flow-matching policy to model arbitrarily complex action distributions in data. Training a flow policy with RL is a tricky problem, due to the iterative nature of the action generation process. We address this challenge by training an expressive one-step policy with RL, rather than directly guiding an iterative flow policy to maximize values. This way, we can completely avoid unstable recursive backpropagation, eliminate costly iterative action generation at test time, yet still mostly maintain expressivity. We experimentally show that FQL leads to strong performance across 73 challenging state- and pixel-based OGBench and D4RL tasks in offline RL and offline-to-online RL. Project page: https://seohong.me/projects/fql/