# Value Flows

arXiv: https://arxiv.org/abs/2510.07650 · HTML: https://mlsanity.com/paper/2510.07650/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 62 of its 85 references that are in the map.
- First posted on arXiv 9 Oct 2025.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 30 of 62)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [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)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [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)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [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)
- [Prioritized Experience Replay](https://mlsanity.com/paper/1511.05952/) (2015)
- [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)
- [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)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [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)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [Efficient Online Reinforcement Learning with Offline Data](https://mlsanity.com/paper/2302.02948/) (2023)
- [IDQL: Implicit Q-Learning as an Actor-Critic Method with Diffusion Policies](https://mlsanity.com/paper/2304.10573/) (2023)

## Built on by (most cited first, 15 of 15)

- [Q-Flow: Stable and Expressive Reinforcement Learning with Flow-Based Policy](https://mlsanity.com/paper/2605.13435/) (2026)
- [Reinforcement Learning via Value Gradient Flow](https://mlsanity.com/paper/2604.14265/) (2026)
- [Scalable Maximum Entropy Reinforcement Learning for Diffusion Policies via Adjoint Matching](https://mlsanity.com/paper/2606.22630/) (2026)
- [Towards Efficient and Expressive Offline RL via Flow-Anchored Noise-conditioned Q-Learning](https://mlsanity.com/paper/2605.01663/) (2026)
- [Path-Coupled Bellman Flows for Distributional Reinforcement Learning](https://mlsanity.com/paper/2605.08253/) (2026)
- [Q-Learning With World Models](https://mlsanity.com/paper/2608.17163/) (2026)
- [Quantile-Coupled Flow Matching for Distributional Reinforcement Learning](https://mlsanity.com/paper/2605.08515/) (2026)
- [Stochastic Actor-Critic: Mitigating Overestimation via Temporal Aleatoric Uncertainty](https://mlsanity.com/paper/2601.00737/) (2026)
- [Distributional Reinforcement Learning with Diffusion Bridge Critics](https://mlsanity.com/paper/2602.05783/) (2026)
- [Horizon Adaptive Offline Policy Learning via Value Stitching](https://mlsanity.com/paper/2606.21136/) (2026)
- [VINE: Taming Generative Control Policies for Reinforcement Learning](https://mlsanity.com/paper/2607.10369/) (2026)
- [Retimed Bellman Flows: Escaping the Impossible Triangle of Velocity Bootstrapping](https://mlsanity.com/paper/2609.32828/) (2026)
- [From Suboptimal to Optimal: One-Step Latent Flow Policies for Offline Reinforcement Learning](https://mlsanity.com/paper/2610.16984/) (2026)
- [Posterior-Averaged Bellman Flow Matching for Distributional Critics](https://mlsanity.com/paper/2610.17788/) (2026)
- [Occupancy Modeling via Drifting: One-Step Generation Enables Direct Policy Extraction](https://mlsanity.com/paper/2610.19883/) (2026)

## Abstract (arXiv)

While most reinforcement learning methods today flatten the distribution of future returns to a single scalar value, distributional RL methods exploit the return distribution to provide stronger learning signals and to enable applications in exploration and safe RL. While the predominant method for estimating the return distribution is by modeling it as a categorical distribution over discrete bins or estimating a finite number of quantiles, such approaches leave unanswered questions about the fine-grained structure of the return distribution and about how to distinguish states with high return uncertainty for decision-making. The key idea in this paper is to use modern, flexible flow-based models to estimate the full future return distributions and identify those states with high return variance. We do so by formulating a new flow-matching objective that generates probability density paths satisfying the distributional Bellman equation. Building upon the learned flow models, we estimate the return uncertainty of distinct states using a new flow derivative ODE. We additionally use this uncertainty information to prioritize learning a more accurate return estimation on certain transitions. We compare our method (Value Flows) with prior methods in the offline and online-to-online settings. Experiments on 37 state-based and 25 image-based benchmark tasks demonstrate that Value Flows achieves a 1.3× improvement on average in success rates. Website: https://pd-perry.github.io/value-flows Code: https://github.com/chongyi-zheng/value-flows