Diff-PCR: Diffusion-Based Correspondence Searching in Doubly Stochastic Matrix Space for Point Cloud Registration

Efficiently finding optimal correspondences between point clouds is crucial for solving both rigid and non-rigid point cloud registration problems. Existing methods often rely on geometric or semantic feature embedding to establish correspondences and estimate transformations or flow fields. Recently, state-of-the-art methods have employed RAFT-like iterative updates to refine the solution. However, these methods have certain limitations. Firstly, their iterative refinement design lacks transparency, and their iterative updates follow a fixed path during the refinement process, which can lead to suboptimal results. Secondly, these methods overlook the importance of refining or optimizing correspondences (or matching matrices) as a precursor to solving transformations or flow fields. They typically compute candidate correspondences based on distances in the point feature space. However, they only project the candidate matching matrix into some matrix space once with Sinkhorn or dual softmax operations to obtain final correspondences. This one-shot projected matching matrix may be far from the globally optimal one, and these approaches do not consider the distribution of the target matching matrix. In this paper, we propose a novel approach that exploits the Denoising Diffusion Model to predict a searching gradient for the optimal matching matrix within the Doubly Stochastic Matrix Space. During the reverse denoising process, our method iteratively searches for better solutions along this denoising gradient, which points towards the maximum likelihood direction of the target matching matrix. Our method offers flexibility by allowing the search to start from any initial matching matrix provided by the online backbone or white noise. Experimental evaluations on the 3DMatch/3DLoMatch and 4DMatch/4DLoMatch datasets demonstrate the effectiveness of our newly designed framework.