  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 nontrivial 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. The code will be made public upon publication.
