# Levy-Driven Correspondence Estimation for Registration

arXiv: https://arxiv.org/abs/2609.32612 · HTML: https://mlsanity.com/paper/2609.32612/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 39 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 25 of 25)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [PREDATOR: Registration of 3D Point Clouds with Low Overlap](https://mlsanity.com/paper/2011.13005/) (2020)
- [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)
- [PointDSC: Robust Point Cloud Registration using Deep Spatial Consistency](https://mlsanity.com/paper/2103.05465/) (2021)
- [FLOT: Scene Flow on Point Clouds Guided by Optimal Transport](https://mlsanity.com/paper/2007.11142/) (2020)
- [REGTR: End-to-end Point Cloud Correspondences with Transformers](https://mlsanity.com/paper/2203.14517/) (2022)
- [Generator Matching: Generative modeling with arbitrary Markov processes](https://mlsanity.com/paper/2410.20587/) (2024)
- [Lepard: Learning partial point cloud matching in rigid and deformable scenes](https://mlsanity.com/paper/2111.12591/) (2021)
- [3D Registration with Maximal Cliques](https://mlsanity.com/paper/2305.10854/) (2023)
- [Rotation-Invariant Transformer for Point Cloud Matching](https://mlsanity.com/paper/2303.08231/) (2023)
- [SC^2-PCR: A Second Order Spatial Compatibility for Efficient and Robust Point Cloud Registration](https://mlsanity.com/paper/2203.14453/) (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)
- [Robust Outlier Rejection for 3D Registration with Variational Bayes](https://mlsanity.com/paper/2304.01514/) (2023)
- [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)
- [HyperGCT: A Dynamic Hyper-GNN-Learned Geometric Constraint for 3D Registration](https://mlsanity.com/paper/2503.02195/) (2025)
- [FUSER: Feed-Forward MUltiview 3D Registration Transformer and SE(3)N Diffusion Refinement](https://mlsanity.com/paper/2512.09373/) (2025)
- [Schr"odinger Bridge Problem for Jump Diffusions](https://mlsanity.com/paper/2411.13765/) (2024)
- [SGMatch: Semantic-Guided Non-Rigid Shape Matching with Flow Regularization](https://mlsanity.com/paper/2603.12937/) (2026)

## Abstract (arXiv)

Finding reliable point correspondences is difficult when point clouds have low overlap or undergo non-rigid deformation. Iterative refinement can correct uncertain matches, but costly network evaluations limit the number of updates. We present LevyMatch, a L'evy-driven method that uses random jumps to refine a soft matching matrix. At each step, a network uses the current matching state and geometric information to predict a target matching matrix. A Brownian reference bridge gives an explicit formula for the update toward this target. A Gamma random clock sets the time step for each update. The updated matches provide new geometric feedback for the next target prediction. We further propose a fixed front-loaded Gamma policy that assigns more expected clock time to early updates and less to later ones, without retraining or extra network evaluations. Reordering the same sampled Gamma increments shows that placing larger increments early gives higher accuracy than placing them late. On 4DMatch and 4DLoMatch, our method improves both non-rigid feature matching recall (NFMR) and inlier ratio (IR) over the compared methods. The front-loaded policy achieves 93.09% NFMR and 92.11% IR on 4DMatch, and 82.79% NFMR and 79.07% IR on 4DLoMatch.