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

Offline reinforcement learning improves robotic policies using previously collected data without further environment interaction. Yet prevalent diffusion- and flow-matching robot policies lack tractable likelihoods, limiting their use in likelihood-based offline RL post-training. AR-NFs offer both expressive action modeling and exact likelihood evaluation, but their sequential sampling incurs substantial sampling overhead during policy optimization and deployment. We present RoMAN-Flow (Robotic Manipulation with Autoregressive Normalizing Flows), an offline reinforcement learning framework that makes AR-NF policies practical for robotic manipulation by addressing this sampling bottleneck in both stages. During policy optimization, RoMAN-Flow employs a sampling-free, advantage-weighted likelihood objective that assigns higher likelihood to high-advantage actions from the offline dataset without sampling from the autoregressive policy. For efficient deployment, it distills the optimized autoregressive policy into a one-step action generator, enabling low-latency action prediction. Experiments across multiple simulated manipulation benchmarks and real-world robotic platforms demonstrate that RoMAN-Flow achieves competitive policy performance while substantially reducing inference latency. Code is available at https://github.com/konnyaku28/RoMAN-Flow.

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.

Diffusion policies effectively model multimodal action distributions for robotic manipulation, but their iterative denoising requires tens to hundreds of network function evaluations (NFEs) for each control prediction, limiting their applicability to high-frequency closed-loop control and online reinforcement learning (RL). We present a two-stage framework for native one-step generative policies that transfers iterative refinement from inference to training. First, Drift-Based Policy (DBP) uses a fixed-point drifting objective to internalize corrective dynamics into the model parameters, producing multimodal action chunks with a single network evaluation by design. Second, Drift-Based Policy Optimization (DBPO) augments the pretrained backbone with a stochastic interface that provides exact conditional rollout likelihoods for PPO-style on-policy updates while preserving 1-NFE deployment. On the 12-task Diffusion Policy suite, DBP improves the average success rate from 0.79 to 0.83 while reducing inference from 100 NFEs to 1. Across 37 point-cloud manipulation tasks, DBP achieves an average success rate of 88.4%, surpassing the leading 1-NFE baseline OMP at 82.3%. DBPO further improves pretrained one-step policies through stable online fine-tuning on RoboMimic and D4RL. On a physical dual-arm UR5 platform, DBP achieves 123/150 successes (82%) with an average end-to-end latency of 9.5 ms, compared with MP1's 89/150 successes (59%) under the same setup. Code is available at https://github.com/YuxuanGao0822/DBPO.