# Extremum Flow Matching for Offline Goal Conditioned Reinforcement Learning

arXiv: https://arxiv.org/abs/2505.19717 · HTML: https://mlsanity.com/paper/2505.19717/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 42 of its 50 references that are in the map.
- First posted on arXiv 26 May 2025.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- Offline RL and imitation learning from data / [Diffusion and flow policies for offline RL](https://mlsanity.com/offlinerl/diffusion-and-flow-policies-for-offline-rl/)

## Builds on (most cited first, 30 of 42)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [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)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Hindsight Experience Replay](https://mlsanity.com/paper/1707.01495/) (2017)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [CALVIN: A Benchmark for Language-Conditioned Policy Learning for Long-Horizon Robot Manipulation Tasks](https://mlsanity.com/paper/2112.03227/) (2021)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [Learning Latent Plans from Play](https://mlsanity.com/paper/1903.01973/) (2019)
- [Contrastive Learning as Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2206.07568/) (2022)
- [NoMaD: Goal Masked Diffusion Policies for Navigation and Exploration](https://mlsanity.com/paper/2310.07896/) (2023)
- [OGBench: Benchmarking Offline Goal-Conditioned RL](https://mlsanity.com/paper/2410.20092/) (2024)
- [Goal-Conditioned Imitation Learning using Score-based Diffusion Policies](https://mlsanity.com/paper/2304.02532/) (2023)
- [MimicPlay: Long-Horizon Imitation Learning by Watching Human Play](https://mlsanity.com/paper/2302.12422/) (2023)
- [Flow Q-Learning](https://mlsanity.com/paper/2502.02538/) (2025)
- [Goal-conditioned Imitation Learning](https://mlsanity.com/paper/1906.05838/) (2019)
- [HIQL: Offline Goal-Conditioned RL with Latent States as Actions](https://mlsanity.com/paper/2307.11949/) (2023)
- [Multimodal Diffusion Transformer: Learning Versatile Behavior from Multimodal Goals](https://mlsanity.com/paper/2407.05996/) (2024)
- [Optimal Goal-Reaching Reinforcement Learning via Quasimetric Learning](https://mlsanity.com/paper/2304.01203/) (2023)
- [FlowPolicy: Enabling Fast and Robust 3D Flow-based Policy via Consistency Flow Matching for Robot Manipulation](https://mlsanity.com/paper/2412.04987/) (2024)
- [From Play to Policy: Conditional Behavior Generation from Uncurated Robot Data](https://mlsanity.com/paper/2210.10047/) (2022)
- [Generative Skill Chaining: Long-Horizon Skill Planning with Diffusion Models](https://mlsanity.com/paper/2401.03360/) (2023)
- [Learning from Reward-Free Offline Data: A Case for Planning with Latent Dynamics Models](https://mlsanity.com/paper/2502.14819/) (2025)

## Built on by (most cited first, 3 of 3)

- [Towards Deploying VLA without Fine-Tuning: Plug-and-Play Inference-Time VLA Policy Steering via Embodied Evolutionary Diffusion](https://mlsanity.com/paper/2511.14178/) (2025)
- [Flow Matching Policy Optimization with Mirror Descent and Entropy Constraints](https://mlsanity.com/paper/2603.17685/) (2026)
- [Native Extrapolation Awareness in Flow-Based Conditional Generation](https://mlsanity.com/paper/2602.13061/) (2026)

## Abstract (arXiv)

Imitation learning is a promising approach for enabling generalist capabilities in humanoid robots, but its scaling is fundamentally constrained by the scarcity of high-quality expert demonstrations. This limitation can be mitigated by leveraging suboptimal, open-ended play data, often easier to collect and offering greater diversity. This work builds upon recent advances in generative modeling, specifically Flow Matching, an alternative to Diffusion models. We introduce a method for estimating the minimum or maximum of the learned distribution by leveraging the unique properties of Flow Matching, namely, deterministic transport and support for arbitrary source distributions. We apply this method to develop several goal-conditioned imitation and reinforcement learning algorithms based on Flow Matching, where policies are conditioned on both current and goal observations. We explore and compare different architectural configurations by combining core components, such as critic, planner, actor, or world model, in various ways. We evaluated our agents on the OGBench benchmark and analyzed how different demonstration behaviors during data collection affect performance in a 2D non-prehensile pushing task. Furthermore, we validated our approach on real hardware by deploying it on the Talos humanoid robot to perform complex manipulation tasks based on high-dimensional image observations, featuring a sequence of pick-and-place and articulated object manipulation in a realistic kitchen environment. Experimental videos and code are available at: https://hucebot.github.io/extremum_flow_matching_website/