  We propose a new framework that formulates point cloud registration as a
denoising diffusion process from noisy transformation to object transformation.
During training stage, object transformation diffuses from ground-truth
transformation to random distribution, and the model learns to reverse this
noising process. In sampling stage, the model refines randomly generated
transformation to the output result in a progressive way. We derive the
variational bound in closed form for training and provide implementations of
the model. Our work provides the following crucial findings: (i) In contrast to
most existing methods, our framework, Diffusion Probabilistic Models for Point
Cloud Registration (PCRDiffusion) does not require repeatedly update source
point cloud to refine the predicted transformation. (ii) Point cloud
registration, one of the representative discriminative tasks, can be solved by
a generative way and the unified probabilistic formulation. Finally, we discuss
and provide an outlook on the application of diffusion model in different
scenarios for point cloud registration. Experimental results demonstrate that
our model achieves competitive performance in point cloud registration. In
correspondence-free and correspondence-based scenarios, PCRDifussion can both
achieve exceeding 50\% performance improvements.
