  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.
