# Learning Robotic Manipulation Policies from Point Clouds with Conditional Flow Matching

arXiv: https://arxiv.org/abs/2409.07343 · HTML: https://mlsanity.com/paper/2409.07343/

## Key facts

- Cited by 65 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 30 of its 33 references that are in the map.
- First posted on arXiv 11 Sep 2024.

## 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 / [Robot manipulation imitation learning](https://mlsanity.com/offlinerl/robot-manipulation-imitation-learning/)

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [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)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [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)
- [RLBench: The Robot Learning Benchmark & Learning Environment](https://mlsanity.com/paper/1909.12271/) (2019)
- [Perceiver-Actor: A Multi-Task Transformer for Robotic Manipulation](https://mlsanity.com/paper/2209.05451/) (2022)
- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [SE(3)-Stochastic Flow Matching for Protein Backbone Generation](https://mlsanity.com/paper/2310.02391/) (2023)
- [Act3D: 3D Feature Field Transformers for Multi-Task Robotic Manipulation](https://mlsanity.com/paper/2306.17817/) (2023)
- [A micro Lie theory for state estimation in robotics](https://mlsanity.com/paper/1812.01537/) (2018)
- [Hierarchical Diffusion Policy for Kinematics-Aware Multi-Task Robotic Manipulation](https://mlsanity.com/paper/2403.03890/) (2024)
- [Deep Regression on Manifolds: A 3D Rotation Case Study](https://mlsanity.com/paper/2103.16317/) (2021)
- [Riemannian Flow Matching Policy for Robot Motion Learning](https://mlsanity.com/paper/2403.10672/) (2024)
- [Interactive Imitation Learning in Robotics: A Survey](https://mlsanity.com/paper/2211.00600/) (2022)
- [AdaFlow: Imitation Learning with Variance-Adaptive Flow-Based Policies](https://mlsanity.com/paper/2402.04292/) (2024)
- [Learning with 3D rotations, a hitchhiker's guide to SO(3)](https://mlsanity.com/paper/2404.11735/) (2024)
- [DITTO: Demonstration Imitation by Trajectory Transformation](https://mlsanity.com/paper/2403.15203/) (2024)
- [Flow Matching Imitation Learning for Multi-Support Manipulation](https://mlsanity.com/paper/2407.12381/) (2024)
- [Correct Me if I am Wrong: Interactive Learning for Robotic Manipulation](https://mlsanity.com/paper/2110.03316/) (2021)
- [The Treachery of Images: Bayesian Scene Keypoints for Deep Policy Learning in Robotic Manipulation](https://mlsanity.com/paper/2305.04718/) (2023)

## Built on by (most cited first, 30 of 65)

- [ManiFlow: A General Robot Manipulation Policy via Consistency Flow Training](https://mlsanity.com/paper/2509.01819/) (2025)
- [Much Ado About Noising: Dispelling the Myths of Generative Robotic Control](https://mlsanity.com/paper/2512.01809/) (2025)
- [3D FlowMatch Actor: Unified 3D Policy for Single- and Dual-Arm Manipulation](https://mlsanity.com/paper/2508.11002/) (2025)
- [Articulated Object Estimation in the Wild](https://mlsanity.com/paper/2509.01708/) (2025)
- [Fast and Robust Visuomotor Riemannian Flow Matching Policy](https://mlsanity.com/paper/2412.10855/) (2024)
- [Chain-of-Action: Trajectory Autoregressive Modeling for Robotic Manipulation](https://mlsanity.com/paper/2506.09990/) (2025)
- [FreqPolicy: Efficient Flow-based Visuomotor Policy via Frequency Consistency](https://mlsanity.com/paper/2506.08822/) (2025)
- [FlowRAM: Grounding Flow Matching Policy with Region-Aware Mamba Framework for Robotic Manipulation](https://mlsanity.com/paper/2506.16201/) (2025)
- [FlowNav: Combining Flow Matching and Depth Priors for Efficient Navigation](https://mlsanity.com/paper/2411.09524/) (2024)
- [Rethinking Bimanual Robotic Manipulation: Learning with Decoupled Interaction Framework](https://mlsanity.com/paper/2503.09186/) (2025)
- [SafeFlowMatcher: Safe and Fast Planning using Flow Matching with Control Barrier Functions](https://mlsanity.com/paper/2509.24243/) (2025)
- [PointMapPolicy: Structured Point Cloud Processing for Multi-Modal Imitation Learning](https://mlsanity.com/paper/2510.20406/) (2025)
- [Fast Flow-based Visuomotor Policies via Conditional Optimal Transport Couplings](https://mlsanity.com/paper/2505.01179/) (2025)
- [Conditioning Matters: Training Diffusion Policies is Faster Than You Think](https://mlsanity.com/paper/2505.11123/) (2025)
- [Uncertainty Comes for Free: Human-in-the-Loop Policies with Diffusion Models](https://mlsanity.com/paper/2503.01876/) (2025)
- [DM1: MeanFlow with Dispersive Regularization for 1-Step Robotic Manipulation](https://mlsanity.com/paper/2510.07865/) (2025)
- [One-Step Flow Policy: Self-Distillation for Fast Visuomotor Policies](https://mlsanity.com/paper/2603.12480/) (2026)
- [UniConFlow: A Unified Constrained Flow-Matching Framework for Certified Motion Planning](https://mlsanity.com/paper/2506.02955/) (2025)
- [Time-Unified Diffusion Policy with Action Discrimination for Robotic Manipulation](https://mlsanity.com/paper/2506.09422/) (2025)
- [Scaling Single Human Demonstrations for Imitation Learning using Generative Foundational Models](https://mlsanity.com/paper/2602.12734/) (2026)
- [From Flow to One Step: Real-Time Multi-Modal Trajectory Policies via Implicit Maximum Likelihood Estimation-based Distribution Distillation](https://mlsanity.com/paper/2603.09415/) (2026)
- [WarmPrior: Straightening Flow-Matching Policies with Temporal Priors](https://mlsanity.com/paper/2605.13959/) (2026)
- [Flow Matching Ergodic Coverage](https://mlsanity.com/paper/2504.17872/) (2025)
- [The Unreasonable Effectiveness of Discrete-Time Gaussian Process Mixtures for Robot Policy Learning](https://mlsanity.com/paper/2505.03296/) (2025)
- [Flow with the Force Field: Learning 3D Compliant Flow Matching Policies from Force and Demonstration-Guided Simulation Data](https://mlsanity.com/paper/2510.02738/) (2025)
- [Designing for Difference: How Human Characteristics Shape Perceptions of Collaborative Robots](https://mlsanity.com/paper/2507.16480/) (2025)
- [Formal Safety Verification and Refinement for Generative Motion Planners via Certified Local Stabilization](https://mlsanity.com/paper/2509.19688/) (2025)
- [ResponsibleRobotBench: Benchmarking Responsible Robot Manipulation using Multi-modal Large Language Models](https://mlsanity.com/paper/2512.04308/) (2025)
- [Crowd-FM: Learned Optimal Selection of Conditional Flow Matching-generated Trajectories for Crowd Navigation](https://mlsanity.com/paper/2602.06698/) (2026)
- [Truncated Rectified Flow Policy for Reinforcement Learning with One-Step Sampling](https://mlsanity.com/paper/2604.09159/) (2026)

## Abstract (arXiv)

Learning from expert demonstrations is a promising approach for training robotic manipulation policies from limited data. However, imitation learning algorithms require a number of design choices ranging from the input modality, training objective, and 6-DoF end-effector pose representation. Diffusion-based methods have gained popularity as they enable predicting long-horizon trajectories and handle multimodal action distributions. Recently, Conditional Flow Matching (CFM) (or Rectified Flow) has been proposed as a more flexible generalization of diffusion models. In this paper, we investigate the application of CFM in the context of robotic policy learning and specifically study the interplay with the other design choices required to build an imitation learning algorithm. We show that CFM gives the best performance when combined with point cloud input observations. Additionally, we study the feasibility of a CFM formulation on the SO(3) manifold and evaluate its suitability with a simplified example. We perform extensive experiments on RLBench which demonstrate that our proposed PointFlowMatch approach achieves a state-of-the-art average success rate of 67.8% over eight tasks, double the performance of the next best method.