# FlowMP: Learning Motion Fields for Robot Planning with Conditional Flow Matching arXiv: https://arxiv.org/abs/2503.06135 ยท HTML: https://mlsanity.com/paper/2503.06135/ ## Key facts - Cited by 15 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 26 of its 43 references that are in the map. - First posted on arXiv 8 Mar 2025. ## Placed in - Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/) ## Builds on (most cited first, 26 of 26) - [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (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) - [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023) - [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022) - [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018) - [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016) - [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023) - [Goal-Conditioned Imitation Learning using Score-based Diffusion Policies](https://mlsanity.com/paper/2304.02532/) (2023) - [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023) - [Flow as the Cross-Domain Manipulation Interface](https://mlsanity.com/paper/2407.15208/) (2024) - [SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusion](https://mlsanity.com/paper/2209.03855/) (2022) - [DALL-E-Bot: Introducing Web-Scale Diffusion Models to Robotics](https://mlsanity.com/paper/2210.02438/) (2022) - [SafeDiffuser: Safe Planning with Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.00148/) (2023) - [Equivariant Diffusion Policy](https://mlsanity.com/paper/2407.01812/) (2024) - [Riemannian Flow Matching Policy for Robot Motion Learning](https://mlsanity.com/paper/2403.10672/) (2024) - [Affordance-based Robot Manipulation with Flow Matching](https://mlsanity.com/paper/2409.01083/) (2024) - [Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference](https://mlsanity.com/paper/1707.07383/) (2017) - [Motion Planning Diffusion: Learning and Adapting Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2412.19948/) (2024) - [ActionFlow: Equivariant, Accurate, and Efficient Policies with Spatially Symmetric Flow Matching](https://mlsanity.com/paper/2409.04576/) (2024) - [Learning Implicit Priors for Motion Optimization](https://mlsanity.com/paper/2204.05369/) (2022) - [DexGrasp-Diffusion: Diffusion-based Unified Functional Grasp Synthesis Method for Multi-Dexterous Robotic Hands](https://mlsanity.com/paper/2407.09899/) (2024) - [Variational Inference MPC using Normalizing Flows and Out-of-Distribution Projection](https://mlsanity.com/paper/2205.04667/) (2022) - [Memory of Motion for Warm-starting Trajectory Optimization](https://mlsanity.com/paper/1907.01474/) (2019) - [VP-STO: Via-point-based Stochastic Trajectory Optimization for Reactive Robot Behavior](https://mlsanity.com/paper/2210.04067/) (2022) - [APEX: Ambidextrous Dual-Arm Robotic Manipulation Using Collision-Free Generative Diffusion Models](https://mlsanity.com/paper/2404.02284/) (2024) ## Built on by (most cited first, 15 of 15) - [Diffusion Models for Robotic Manipulation: A Survey](https://mlsanity.com/paper/2504.08438/) (2025) - [Much Ado About Noising: Dispelling the Myths of Generative Robotic Control](https://mlsanity.com/paper/2512.01809/) (2025) - [FlowDrive: moderated flow matching with data balancing for trajectory planning](https://mlsanity.com/paper/2509.21961/) (2025) - [From Noise to Intent: Anchoring Generative VLA Policies with Residual Bridges](https://mlsanity.com/paper/2604.21391/) (2026) - [FLASH: Efficient Visuomotor Policy via Sparse Sampling](https://mlsanity.com/paper/2605.15492/) (2026) - [Causal Flow Q-Learning for Robust Offline Reinforcement Learning](https://mlsanity.com/paper/2602.02847/) (2026) - [DreamFlow: Local Navigation Beyond Observation via Conditional Flow Matching in the Latent Space](https://mlsanity.com/paper/2603.02976/) (2026) - [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026) - [Flow Motion Policy: Manipulator Motion Planning with Flow Matching Models](https://mlsanity.com/paper/2604.07084/) (2026) - [Frequency-Aware Flow Matching for Continuous and Consistent Robotic Action Generation](https://mlsanity.com/paper/2606.20135/) (2026) - [Model Tensor Planning](https://mlsanity.com/paper/2505.01059/) (2025) - [Flow-Opt: Scalable Centralized Multi-Robot Trajectory Optimization with Flow Matching and Differentiable Optimization](https://mlsanity.com/paper/2510.09204/) (2025) - [DynFly: Dynamic-Aware Continuous Trajectory Generation for UAV Vision-Language Navigation in Urban Environments](https://mlsanity.com/paper/2606.31654/) (2026) - [BridgeFlow: Fast and Robust SE(2)-Equivariant Motion Planning with Flow Matching](https://mlsanity.com/paper/2607.14725/) (2026) - [DROM: A Language-Guided Diffusion Framework for Multi-Skill Robotic Manipulation](https://mlsanity.com/paper/2609.37348/) (2026) ## Abstract (arXiv) Prior flow matching methods in robotics have primarily learned velocity fields to morph one distribution of trajectories into another. In this work, we extend flow matching to capture second-order trajectory dynamics, incorporating acceleration effects either explicitly in the model or implicitly through the learning objective. Unlike diffusion models, which rely on a noisy forward process and iterative denoising steps, flow matching trains a continuous transformation (flow) that directly maps a simple prior distribution to the target trajectory distribution without any denoising procedure. By modeling trajectories with second-order dynamics, our approach ensures that generated robot motions are smooth and physically executable, avoiding the jerky or dynamically infeasible trajectories that first-order models might produce. We empirically demonstrate that this second-order conditional flow matching yields superior performance on motion planning benchmarks, achieving smoother trajectories and higher success rates than baseline planners. These findings highlight the advantage of learning acceleration-aware motion fields, as our method outperforms existing motion planning methods in terms of trajectory quality and planning success.