# Q-Flow: Stable and Expressive Reinforcement Learning with Flow-Based Policy

arXiv: https://arxiv.org/abs/2605.13435 · HTML: https://mlsanity.com/paper/2605.13435/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in RL with diffusion and flow models, one of 15 directions in Deep reinforcement learning methods.
- Builds on 49 of its 56 references that are in the map.
- First posted on arXiv 13 May 2026.

## Placed in

- 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 49)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (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)
- [A Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06860/) (2021)
- [Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction](https://mlsanity.com/paper/1906.00949/) (2019)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [Behavior Regularized Offline Reinforcement Learning](https://mlsanity.com/paper/1911.11361/) (2019)
- [Offline Reinforcement Learning as One Big Sequence Modeling Problem](https://mlsanity.com/paper/2106.02039/) (2021)
- [MOReL : Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2005.05951/) (2020)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Models](https://mlsanity.com/paper/2305.16381/) (2023)
- [IDQL: Implicit Q-Learning as an Actor-Critic Method with Diffusion Policies](https://mlsanity.com/paper/2304.10573/) (2023)
- [Diffusion Policy Policy Optimization](https://mlsanity.com/paper/2409.00588/) (2024)
- [OGBench: Benchmarking Offline Goal-Conditioned RL](https://mlsanity.com/paper/2410.20092/) (2024)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [Flow Q-Learning](https://mlsanity.com/paper/2502.02538/) (2025)
- [Offline Reinforcement Learning via High-Fidelity Generative Behavior Modeling](https://mlsanity.com/paper/2209.14548/) (2022)
- [Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learning](https://mlsanity.com/paper/2304.12824/) (2023)
- [Learning a Diffusion Model Policy from Rewards via Q-Score Matching](https://mlsanity.com/paper/2312.11752/) (2023)

## Built on by (most cited first, 6 of 6)

- [Critic-Free Pretraining for Efficient Online Reinforcement Learning Fine-Tuning](https://mlsanity.com/paper/2608.10473/) (2026)
- [DIA: Denoising Intermediate Advantage for Diffusion Policy Optimization](https://mlsanity.com/paper/2609.12245/) (2026)
- [Adjoint Guidance Flow: Amortized Critic Guidance for VLA Policies](https://mlsanity.com/paper/2609.34944/) (2026)
- [Diffusion Policy Improvement with Proposal-Conditioned Refinement Flows](https://mlsanity.com/paper/2609.36812/) (2026)
- [Reinforcement Learning via Fixed-point Flow Matching](https://mlsanity.com/paper/2610.12848/) (2026)
- [Value-Guided Repulsion for Offline Reinforcement Learning](https://mlsanity.com/paper/2610.20190/) (2026)

## Abstract (arXiv)

There is growing interest in utilizing flow-based models as decision-making policies in reinforcement learning due to their high expressive capacity. However, effectively leveraging this expressivity for value maximization remains challenging, as naive gradient-based optimization requires backpropagating through numerical solvers and often leads to instability. Existing approaches typically address this issue by restricting the expressive capacity of flow-based policies, resulting in a trade-off between optimization stability and representational flexibility. To resolve this, we introduce Q-Flow, a framework that leverages the deterministic nature of flow dynamics to explicitly propagate terminal trajectory value to intermediate latent states along the policy-induced flow. This formulation enables stable policy optimization using intermediate value gradients without unrolling the numerical solver, effectively bridging the gap between stability and expressivity. We evaluate Q-Flow in the offline learning setting on the challenging OGBench suite, where it consistently outperforms state-of-the-art baselines by an average of 10.6 percentage points, while also enabling stable online adaptation within the same framework.