mlsanityData to 14 Oct 2026

Riemannian Flow Matching Policy for Robot Motion Learning

arXiv 2403.10672 ↗First posted 15 Mar 2024cs.RO cs.LGcited by 63

On the map: Diffusion models → Diffusion and flow policies for robotics

Abstract (arXiv)

We introduce Riemannian Flow Matching Policies (RFMP), a novel model for learning and synthesizing robot visuomotor policies. RFMP leverages the efficient training and inference capabilities of flow matching methods. By design, RFMP inherits the strengths of flow matching: the ability to encode high-dimensional multimodal distributions, commonly encountered in robotic tasks, and a very simple and fast inference process. We demonstrate the applicability of RFMP to both state-based and vision-conditioned robot motion policies. Notably, as the robot state resides on a Riemannian manifold, RFMP inherently incorporates geometric awareness, which is crucial for realistic robotic tasks. To evaluate RFMP, we conduct two proof-of-concept experiments, comparing its performance against Diffusion Policies. Although both approaches successfully learn the considered tasks, our results show that RFMP provides smoother action trajectories with significantly lower inference times.

Key facts. Cited by 63 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 25 of its 34 references that are in the map. First posted on arXiv 15 Mar 2024.

Builds on

25 of 34 references.

Closest ancestors · 3

Same direction, newest first

  1. 2023Goal-Conditioned Imitation Learning using Score-based Diffusion Policies5 Apr
  2. 2023Diffusion Policy: Visuomotor Policy Learning via Action Diffusion7 Mar
  3. 2022Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning12 Aug

Other references · 22

  1. 2022Flow Matching for Generative Modelingcited by 5,702
  2. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
  3. 2018Group Normalizationcited by 1,524
  4. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
  5. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,114
  6. 2022Planning with Diffusion for Flexible Behavior Synthesiscited by 1,061
  7. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 879
  8. 2021What Matters in Learning from Offline Human Demonstrations for Robot Manipulationcited by 725
  9. 2022Understanding Diffusion Models: A Unified Perspectivecited by 340
  10. 2023Flow Matching on General Geometriescited by 265
  11. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 150
  12. 2022Riemannian Diffusion Modelscited by 122
10 more
  1. 2022Efficient Video Prediction via Sparsely Conditioned Flow Matchingcited by 55
  2. 2023Generative Pre-training for Speech with Flow Matchingcited by 55
  3. 2020ImitationFlow: Learning Deep Stable Stochastic Dynamic Systems by Normalizing Flowscited by 33
  4. 2020Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systemscited by 32
  5. 2023Scaling Riemannian Diffusion Modelscited by 18
  6. 2022Learning Riemannian Stable Dynamical Systems via Diffeomorphismscited by 17
  7. 2021Learning Stable Vector Fields on Lie Groupscited by 12
  8. 2020Learning Stable Normalizing-Flow Control for Robotic Manipulationcited by 9
  9. 2022Wrapped Distributions on homogeneous Riemannian manifoldscited by 9
  10. 2023Unraveling the Single Tangent Space Fallacy: An Analysis and Clarification for Applying Riemannian Geometry in Robot Learningcited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 6; 2025: 29; 2026: 28.

63 papers.

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  1. 2025Real-Time Execution of Action Chunking Flow Policiescited by 216
  2. 2025ReinFlow: Fine-tuning Flow Matching Policy with Online Reinforcement Learningcited by 97
  3. 2024Learning Robotic Manipulation Policies from Point Clouds with Conditional Flow Matchingcited by 65
  4. 2025FLOWER: Democratizing Generalist Robot Policies with Efficient Vision-Language-Action Flow Policiescited by 57
  5. 2024Affordance-based Robot Manipulation with Flow Matchingcited by 54
  6. 2025Can We Detect Failures Without Failure Data? Uncertainty-Aware Runtime Failure Detection for Imitation Learning Policiescited by 52
  7. 2025ManiFlow: A General Robot Manipulation Policy via Consistency Flow Trainingcited by 49
  8. 2025Failure Prediction at Runtime for Generative Robot Policiescited by 42
  9. 2025Streaming Flow Policy: Simplifying diffusion/flow-matching policies by treating action trajectories as flow trajectoriescited by 39
  10. 2024Flow Matching Imitation Learning for Multi-Support Manipulationcited by 29
  11. 2024ActionFlow: Equivariant, Accurate, and Efficient Policies with Spatially Symmetric Flow Matchingcited by 26
  12. 2025VITA: Vision-to-Action Flow Matching Policycited by 25
38 more
  1. 20253D FlowMatch Actor: Unified 3D Policy for Single- and Dual-Arm Manipulationcited by 20
  2. 2026Learning Native Continuation for Action Chunking Flow Policiescited by 19
  3. 2024Fast and Robust Visuomotor Riemannian Flow Matching Policycited by 18
  4. 2025FlowMP: Learning Motion Fields for Robot Planning with Conditional Flow Matchingcited by 15
  5. 2025FlowRAM: Grounding Flow Matching Policy with Region-Aware Mamba Framework for Robotic Manipulationcited by 13
  6. 2026Learning on the Manifold: Unlocking Standard Diffusion Transformers with Representation Encoderscited by 13
  7. 2025SafeFlowMatcher: Safe and Fast Planning using Flow Matching with Control Barrier Functionscited by 12
  8. 2025VFP: Variational Flow-Matching Policy for Multi-Modal Robot Manipulationcited by 9
  9. 2025Riemannian Consistency Modelcited by 8
  10. 2026One-Step Flow Policy: Self-Distillation for Fast Visuomotor Policiescited by 7
  11. 2025UniConFlow: A Unified Constrained Flow-Matching Framework for Certified Motion Planningcited by 5
  12. 2025Energy-Based Flow Matching for Generating 3D Molecular Structurecited by 4
  13. 2025SE(3)-PoseFlow: Estimating 6D Pose Distributions for Uncertainty-Aware Robotic Manipulationcited by 4
  14. 2026WarmPrior: Straightening Flow-Matching Policies with Temporal Priorscited by 4
  15. 2025The Unreasonable Effectiveness of Discrete-Time Gaussian Process Mixtures for Robot Policy Learningcited by 3
  16. 2025Extremum Flow Matching for Offline Goal Conditioned Reinforcement Learningcited by 3
  17. 2025Diffusion-Based Impedance Learning for Contact-Rich Manipulation Taskscited by 3
  18. 2025Diffusion Bridge or Flow Matching? A Unifying Framework and Comparative Analysiscited by 3
  19. 2026GoldenStart: Q-Guided Priors and Entropy Control for Distilling Flow Policiescited by 3
  20. 2024Motion Manifold Flow Primitives for Task-Conditioned Trajectory Generation under Complex Task-Motion Dependenciescited by 2
  21. 2026CoLA-Flow Policy: Temporally Coherent Imitation Learning via Continuous Latent Action Flow Matching for Robotic Manipulationcited by 2
  22. 2026MimicIK: Real-Time Generative Inverse Kinematics from Teleoperation with FK Consistencycited by 2
  23. 2026The Geometry of Flow-Matching Uncertainty: A Cost-free Uncertainty Proxy and Its Application in Flow-based VLA Failure Detectioncited by 2
  24. 2025MSG: Multi-Stream Generative Policies for Sample-Efficient Robotic Manipulationcited by 1
  25. 2025Iterative Refinement of Flow Policies in Probability Space for Online Reinforcement Learningcited by 1
  26. 2025Imitation Learning Policy based on Multi-Step Consistent Integration Shortcut Modelcited by 1
  27. 2025DASIP: Dynamic Test-Time Compute Scaling for Robot Control with Stochastic Interpolant Policiescited by 1
  28. 2026ScoRe-Flow: Complete Distributional Control via Score-Based Reinforcement Learning for Flow Matchingcited by 1
  29. 2026Geodesic Flow Matching for Denoising High-Dimensional Structured Representationscited by 1
  30. 2026Invertible Neural Network Adapter for One-Step Flow Matching in Robot Manipulationcited by 1
  31. 2026Frequency-Aware Flow Matching for Continuous and Consistent Robotic Action Generationcited by 1
  32. 2025Towards Safe Imitation Learning via Potential Field-Guided Flow Matchingcited by 0
  33. 2025Fine-Tuning Flow Matching via Maximum Likelihood Estimation of Reconstructionscited by 0
  34. 2025Learning Robust Visuomotor Policies via Dynamics Alignmentcited by 0
  35. 2025Tensor Gauge Flow Modelscited by 0
  36. 2026DFPO: Scaling Value Modeling via Distributional Flow towards Robust and Generalizable LLM Post-Trainingcited by 0
  37. 2026Recovering Hidden Reward in Diffusion-Based Policiescited by 0
  38. 2026Adversarial Dual On-Policy Distillation from Expressive Teachercited by 0

50 most cited of 63 All 63 (JSON)

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  1. 2019Riemannian Motion Policy Fusion through Learnable Lyapunov Function Reshaping
  2. 2026Trajectory-Consistent Flow Matching for Robust Visuomotor Policy Learning
  3. 2026Latent Diffusion Policy: Shaping Latent Spaces for Diffusion-Based Robotic Manipulation
  4. 2024FlowPolicy: Enabling Fast and Robust 3D Flow-based Policy via Consistency Flow Matching for Robot Manipulation
  5. 2025Fast Flow-based Visuomotor Policies via Conditional Optimal Transport Couplings
  6. 20253D Flow Diffusion Policy: Visuomotor Policy Learning via Generating Flow in 3D Space
  7. 2025RGMP: Recurrent Geometric-prior Multimodal Policy for Generalizable Humanoid Robot Manipulation
  8. 2025Dense-Jump Flow Matching with Non-Uniform Time Scheduling for Robotic Policies: Mitigating Multi-Step Inference Degradation