# Normalizing Flows are Capable Models for Continuous Control

arXiv: https://arxiv.org/abs/2505.23527 · HTML: https://mlsanity.com/paper/2505.23527/

## Key facts

- Cited by 14 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 80 of its 93 references that are in the map.
- First posted on arXiv 29 May 2025.

## 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 80)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [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)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [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)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)

## Built on by (most cited first, 14 of 14)

- [Q-Flow: Stable and Expressive Reinforcement Learning with Flow-Based Policy](https://mlsanity.com/paper/2605.13435/) (2026)
- [NinA: Normalizing Flows in Action. Training VLA Models with Normalizing Flows](https://mlsanity.com/paper/2508.16845/) (2025)
- [SERNF: Sample-Efficient Real-World Dexterous Policy Fine-Tuning via Action-Chunked Critics and Normalizing Flows](https://mlsanity.com/paper/2602.09580/) (2026)
- [GoldenStart: Q-Guided Priors and Entropy Control for Distilling Flow Policies](https://mlsanity.com/paper/2603.14245/) (2026)
- [Causal Flow Q-Learning for Robust Offline Reinforcement Learning](https://mlsanity.com/paper/2602.02847/) (2026)
- [NFTR: From Provable Mode-Averaging to Geodesic Subgoal Selection in Offline Goal-Conditioned RL](https://mlsanity.com/paper/2607.07855/) (2026)
- [Beyond Distributions: Geometric Action Control for Continuous Reinforcement Learning](https://mlsanity.com/paper/2511.08234/) (2025)
- [Data-Efficient Hierarchical Goal-Conditioned Reinforcement Learning via Normalizing Flows](https://mlsanity.com/paper/2602.11142/) (2026)
- [NFPO: Stabilized Policy Optimization of Normalizing Flow for Robotic Policy Learning](https://mlsanity.com/paper/2603.11470/) (2026)
- [Maximum Entropy Behavior Exploration for Sim2Real Zero-Shot Reinforcement Learning](https://mlsanity.com/paper/2603.25464/) (2026)
- [Warp RL: Reshaping Base Policy Distributions for Dynamics Adaptation](https://mlsanity.com/paper/2606.31043/) (2026)
- [DFPO: Scaling Value Modeling via Distributional Flow towards Robust and Generalizable LLM Post-Training](https://mlsanity.com/paper/2602.05890/) (2026)
- [Escaping Offline Pessimism: Vector-Field Reward Shaping for Safe Frontier Exploration](https://mlsanity.com/paper/2603.18326/) (2026)
- [QHyer: Q-conditioned Hybrid Attention-mamba Transformer for Offline Goal-conditioned RL](https://mlsanity.com/paper/2605.01862/) (2026)

## Abstract (arXiv)

Modern reinforcement learning (RL) algorithms have found success by using powerful probabilistic models, such as transformers, energy-based models, and diffusion/flow-based models. To this end, RL researchers often choose to pay the price of accommodating these models into their algorithms -- diffusion models are expressive, but are computationally intensive due to their reliance on solving differential equations, while autoregressive transformer models are scalable but typically require learning discrete representations. Normalizing flows (NFs), by contrast, seem to provide an appealing alternative, as they enable likelihoods and sampling without solving differential equations or autoregressive architectures. However, their potential in RL has received limited attention, partly due to the prevailing belief that normalizing flows lack sufficient expressivity. We show that this is not the case. Building on recent work in NFs, we propose a single NF architecture which integrates seamlessly into RL algorithms, serving as a policy, Q-function, and occupancy measure. Our approach leads to much simpler algorithms, and achieves higher performance in imitation learning, offline, goal conditioned RL and unsupervised RL.