DiffusionPCR: Diffusion Models for Robust Multi-Step Point Cloud Registration

Point Cloud Registration (PCR) estimates the relative rigid transformation between two point clouds. We propose formulating PCR as a denoising diffusion probabilistic process, mapping noisy transformations to the ground truth. However, using diffusion models for PCR has non-trivial challenges, such as adapting a generative model to a discriminative task and leveraging the estimated nonlinear transformation from the previous step. Instead of training a diffusion model to directly map pure noise to ground truth, we map the predictions of an off-the-shelf PCR model to ground truth.The predictions of off-the-shelf models are often imperfect, especially in challenging cases where the two points clouds have low overlap, and thus could be seen as noisy versions of the real rigid transformation. In addition, we transform the rotation matrix into a spherical linear space for interpolation between samples in the forward process, and convert rigid transformations into auxiliary information to implicitly exploit last-step estimations in the reverse process. As a result, conditioned on time step, the denoising model adapts to the increasing accuracy across steps and refines registrations. Our extensive experiments showcase the effectiveness of our DiffusionPCR, yielding state-of-the-art registration recall rates (95.3%/81.6%) on 3DMatch and 3DLoMatch.