# NFPO: Stabilized Policy Optimization of Normalizing Flow for Robotic Policy Learning

arXiv: https://arxiv.org/abs/2603.11470 · HTML: https://mlsanity.com/paper/2603.11470/

## Key facts

- Cited by 1 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 45 of its 52 references that are in the map.
- First posted on arXiv 12 Mar 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 45)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [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)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Octo: An Open-Source Generalist Robot Policy](https://mlsanity.com/paper/2405.12213/) (2024)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [Learning Quadrupedal Locomotion over Challenging Terrain](https://mlsanity.com/paper/2010.11251/) (2020)
- [TD-MPC2: Scalable, Robust World Models for Continuous Control](https://mlsanity.com/paper/2310.16828/) (2023)
- [RMA: Rapid Motor Adaptation for Legged Robots](https://mlsanity.com/paper/2107.04034/) (2021)
- [Learning robust perceptive locomotion for quadrupedal robots in the wild](https://mlsanity.com/paper/2201.08117/) (2022)
- [Orbit: A Unified Simulation Framework for Interactive Robot Learning Environments](https://mlsanity.com/paper/2301.04195/) (2023)
- [Diffusion Policy Policy Optimization](https://mlsanity.com/paper/2409.00588/) (2024)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [OmniH2O: Universal and Dexterous Human-to-Humanoid Whole-Body Teleoperation and Learning](https://mlsanity.com/paper/2406.08858/) (2024)
- [Real-World Humanoid Locomotion with Reinforcement Learning](https://mlsanity.com/paper/2303.03381/) (2023)
- [Rapid Locomotion via Reinforcement Learning](https://mlsanity.com/paper/2205.02824/) (2022)
- [BeyondMimic: From Motion Tracking to Versatile Humanoid Control via Guided Diffusion](https://mlsanity.com/paper/2508.08241/) (2025)
- [Learning a Diffusion Model Policy from Rewards via Q-Score Matching](https://mlsanity.com/paper/2312.11752/) (2023)
- [Deep Whole-Body Control: Learning a Unified Policy for Manipulation and Locomotion](https://mlsanity.com/paper/2210.10044/) (2022)

## Built on by (most cited first, 1 of 1)

- [PrT-Flow: Probability-Tractable Flow Matching for Reinforcement Learning](https://mlsanity.com/paper/2610.17667/) (2026)

## Abstract (arXiv)

Deep Reinforcement Learning (DRL) has experienced significant advancements in recent years and has been widely used in many fields. In DRL-based robotic policy learning, however, current de facto policy parameterization is still multivariate Gaussian (with diagonal covariance matrix), which lacks the ability to model multi-modal distribution. In this work, we explore the adoption of a modern network architecture, i.e. Normalizing Flow (NF) as the policy parameterization for its ability of multi-modal modeling, closed form of log probability and low computation and memory overhead. However, naively training NF in online Reinforcement Learning (RL) usually leads to training instability. We provide a detailed analysis for this phenomenon and successfully address it via simple but effective technique. With extensive experiments in multiple simulation environments, we show our method, NFPO could obtain robust and strong performance in widely used robotic learning tasks and successfully transfer into real-world robots.