# BridgeMatch: Conditional Transport Bridges in Matching Matrix Space for 3D Deformable Registration

arXiv: https://arxiv.org/abs/2609.11472 · HTML: https://mlsanity.com/paper/2609.11472/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 46 of its 59 references that are in the map.
- First posted on arXiv 10 Sep 2026.

## Placed in

- Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/)

## Builds on (most cited first, 30 of 46)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [PREDATOR: Registration of 3D Point Clouds with Low Overlap](https://mlsanity.com/paper/2011.13005/) (2020)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [Geometric Transformer for Fast and Robust Point Cloud Registration](https://mlsanity.com/paper/2202.06688/) (2022)
- [D3Feat: Joint Learning of Dense Detection and Description of 3D Local Features](https://mlsanity.com/paper/2003.03164/) (2020)
- [CoFiNet: Reliable Coarse-to-fine Correspondences for Robust Point Cloud Registration](https://mlsanity.com/paper/2110.14076/) (2021)
- [FLOT: Scene Flow on Point Clouds Guided by Optimal Transport](https://mlsanity.com/paper/2007.11142/) (2020)
- [Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence](https://mlsanity.com/paper/2003.14286/) (2020)
- [Neural Scene Flow Prior](https://mlsanity.com/paper/2111.01253/) (2021)
- [Lepard: Learning partial point cloud matching in rigid and deformable scenes](https://mlsanity.com/paper/2111.12591/) (2021)
- [RoboCraft: Learning to See, Simulate, and Shape Elasto-Plastic Objects with Graph Networks](https://mlsanity.com/paper/2205.02909/) (2022)
- [Rotation-Invariant Transformer for Point Cloud Matching](https://mlsanity.com/paper/2303.08231/) (2023)
- [Non-rigid Point Cloud Registration with Neural Deformation Pyramid](https://mlsanity.com/paper/2205.12796/) (2022)
- [PointPWC-Net: A Coarse-to-Fine Network for Supervised and Self-Supervised Scene Flow Estimation on 3D Point Clouds](https://mlsanity.com/paper/1911.12408/) (2019)
- [Dynamic Point Fields](https://mlsanity.com/paper/2304.02626/) (2023)
- [SE(3) Diffusion Model-based Point Cloud Registration for Robust 6D Object Pose Estimation](https://mlsanity.com/paper/2310.17359/) (2023)
- [Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronization](https://mlsanity.com/paper/2111.12878/) (2021)
- [PARE-Net: Position-Aware Rotation-Equivariant Networks for Robust Point Cloud Registration](https://mlsanity.com/paper/2407.10142/) (2024)
- [P2P-Bridge: Diffusion Bridges for 3D Point Cloud Denoising](https://mlsanity.com/paper/2408.16325/) (2024)
- [Deep Graph-based Spatial Consistency for Robust Non-rigid Point Cloud Registration](https://mlsanity.com/paper/2303.09950/) (2023)
- [Multiway Point Cloud Mosaicking with Diffusion and Global Optimization](https://mlsanity.com/paper/2404.00429/) (2024)
- [Rectified Point Flow: Generic Point Cloud Pose Estimation](https://mlsanity.com/paper/2506.05282/) (2025)
- [TurboReg: TurboClique for Robust and Efficient Point Cloud Registration](https://mlsanity.com/paper/2507.01439/) (2025)
- [Boundary Constraint-free Biomechanical Model-Based Surface Matching for Intraoperative Liver Deformation Correction](https://mlsanity.com/paper/2403.09964/) (2024)
- [Planning with Spatial-Temporal Abstraction from Point Clouds for Deformable Object Manipulation](https://mlsanity.com/paper/2210.15751/) (2022)

## Abstract (arXiv)

Reliable matching between partially observed, deforming point clouds requires global context and fine geometric detail. Coarse candidate selection can exclude correct fine-level correspondences. We present paper, a unified conditional transport framework with the matching matrix itself as the evolving state. Coarse diffusion establishes global matching hypotheses; hierarchy-preserving lifting expands them into a structured high-resolution source. Geometry-conditioned ODE and SDE bridges continue refinement in the complete fine-level candidate space, allowing coarse errors to be corrected. The deterministic endpoint-parameterized conditional flow matching (CFM) design improves matching through iteration, while the SDE forward drift enables effective few-step refinement. Experiments on 4DMatch and 4DLoMatch demonstrate competitive matching and non-rigid registration, with transfer to CAPE and DeepDeform without target-domain training.