# BridgeFlow: Fast and Robust SE(2)-Equivariant Motion Planning with Flow Matching

arXiv: https://arxiv.org/abs/2607.14725 · HTML: https://mlsanity.com/paper/2607.14725/

## Key facts

- No citing papers in the map yet (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 36 references that are in the map.
- First posted on arXiv 16 Jul 2026.

## 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, 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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [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)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Diffusion-based Generation, Optimization, and Planning in 3D Scenes](https://mlsanity.com/paper/2301.06015/) (2023)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [Stochastic interpolants with data-dependent couplings](https://mlsanity.com/paper/2310.03725/) (2023)
- [Motion Planning Networks](https://mlsanity.com/paper/1806.05767/) (2018)
- [EquiBot: SIM(3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learning](https://mlsanity.com/paper/2407.01479/) (2024)
- [Motion Planning Networks: Bridging the Gap Between Learning-based and Classical Motion Planners](https://mlsanity.com/paper/1907.06013/) (2019)
- [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)
- [CFG-Zero*: Improved Classifier-Free Guidance for Flow Matching Models](https://mlsanity.com/paper/2503.18886/) (2025)
- [Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference](https://mlsanity.com/paper/1707.07383/) (2017)
- [EDMP: Ensemble-of-costs-guided Diffusion for Motion Planning](https://mlsanity.com/paper/2309.11414/) (2023)
- [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)
- [ET-SEED: Efficient Trajectory-Level SE(3) Equivariant Diffusion Policy](https://mlsanity.com/paper/2411.03990/) (2024)
- [The Curse of Conditions: Analyzing and Improving Optimal Transport for Conditional Flow-Based Generation](https://mlsanity.com/paper/2503.10636/) (2025)
- [FlowMP: Learning Motion Fields for Robot Planning with Conditional Flow Matching](https://mlsanity.com/paper/2503.06135/) (2025)
- [PRESTO: Fast Motion Planning Using Diffusion Models Based on Key-Configuration Environment Representation](https://mlsanity.com/paper/2409.16012/) (2024)
- [SE(3)-Equivariant Robot Learning and Control: A Tutorial Survey](https://mlsanity.com/paper/2503.09829/) (2025)
- [Constrained Motion Planning Networks X](https://mlsanity.com/paper/2010.08707/) (2020)
- [Structured-Diffuser: Diffusion with Task-Conditioned Structured Priors for Motion Planning](https://mlsanity.com/paper/2509.25685/) (2025)
- [Learning-Based Motion Planning with Mixture Density Networks](https://mlsanity.com/paper/2206.03292/) (2022)
- [Accelerated Multi-Modal Motion Planning Using Context-Conditioned Diffusion Models](https://mlsanity.com/paper/2510.14615/) (2025)

## Abstract (arXiv)

In robotic motion planning, equivariance to rigid body transformations is crucial for robust spatial generalization. However, current learning-based planners face a critical dilemma: they either lack inherent equivariance, treating transformed tasks as novel scenarios, or enforce it via computationally expensive specialized architectures that bottleneck real-time inference. To break this trade-off, we propose BridgeFlow, a fast and strictly SE(2)-equivariant generative motion planning framework. Rather than relying on heavy equivariant networks, BridgeFlow achieves exact spatial equivariance via a lightweight task-centric canonicalization module, enabling generalization using standard architectures. To further accelerate inference, we pair a Brownian bridge informative prior with context-aware mini-batch optimal transport. This constructs a straightened vector field that minimizes transport costs and stabilizes training. Furthermore, environmental awareness is explicitly embedded via Classifier-Free Guidance. Evaluations in dense 2D environments and on a 7-DoF Franka manipulator demonstrate that BridgeFlow achieves up to a 15x inference speedup and a 2x higher valid trajectory rate over state-of-the-art diffusion baselines, alongside robust generalization to entirely unseen environments and arbitrary spatial transformations.