  In this paper, we introduce an SE(3) diffusion model-based point cloud
registration framework for 6D object pose estimation in real-world scenarios.
Our approach formulates the 3D registration task as a denoising diffusion
process, which progressively refines the pose of the source point cloud to
obtain a precise alignment with the model point cloud. Training our framework
involves two operations: An SE(3) diffusion process and an SE(3) reverse
process. The SE(3) diffusion process gradually perturbs the optimal rigid
transformation of a pair of point clouds by continuously injecting noise
(perturbation transformation). By contrast, the SE(3) reverse process focuses
on learning a denoising network that refines the noisy transformation
step-by-step, bringing it closer to the optimal transformation for accurate
pose estimation. Unlike standard diffusion models used in linear Euclidean
spaces, our diffusion model operates on the SE(3) manifold. This requires
exploiting the linear Lie algebra $\mathfrak{se}(3)$ associated with SE(3) to
constrain the transformation transitions during the diffusion and reverse
processes. Additionally, to effectively train our denoising network, we derive
a registration-specific variational lower bound as the optimization objective
for model learning. Furthermore, we show that our denoising network can be
constructed with a surrogate registration model, making our approach applicable
to different deep registration networks. Extensive experiments demonstrate that
our diffusion registration framework presents outstanding pose estimation
performance on the real-world TUD-L, LINEMOD, and Occluded-LINEMOD datasets.
