Diff-Reg: Diffusion Model in Doubly Stochastic Matrix Space for Registration Problem

Qianliang Wu*, Haobo Jiang*, Lei Luo, Jun Li, Yaqing Ding*, Jin Xie*, Jian Yang* ;

"Establishing reliable correspondences is essential for 3D and 2D-3D registration tasks. Existing methods commonly leverage geometric or semantic point features to generate potential correspondences. However, these features may face challenges such as large deformation, scale inconsistency, and ambiguous matching problems (e.g., symmetry). Additionally, many previous methods, which rely on single-pass prediction, may struggle with local minima in complex scenarios. To mitigate these challenges, we introduce a diffusion matching model for robust correspondence construction. Our approach treats correspondence estimation as a denoising diffusion process within the doubly stochastic matrix space, which gradually denoises (refines) a doubly stochastic matching matrix to the ground-truth one for high-quality correspondence estimation. It involves a forward diffusion process that gradually introduces Gaussian noise into the ground truth matching matrix and a reverse denoising process that iteratively refines the noisy one. In particular, we deploy a lightweight denoising strategy during the inference phase. Specifically, once points/image features are extracted and fixed, we utilize them to conduct multiple-pass denoising predictions in the reverse sampling process. Evaluation of our method on both 3D and 2D-3D registration tasks confirms its effectiveness. The code is available at https://github.com/wuqianliang/Diff-Reg."