  We propose a novel approach for probabilistic generative modeling of 3D
shapes. Unlike most existing models that learn to deterministically translate a
latent vector to a shape, our model, Point-Voxel Diffusion (PVD), is a unified,
probabilistic formulation for unconditional shape generation and conditional,
multi-modal shape completion. PVD marries denoising diffusion models with the
hybrid, point-voxel representation of 3D shapes. It can be viewed as a series
of denoising steps, reversing the diffusion process from observed point cloud
data to Gaussian noise, and is trained by optimizing a variational lower bound
to the (conditional) likelihood function. Experiments demonstrate that PVD is
capable of synthesizing high-fidelity shapes, completing partial point clouds,
and generating multiple completion results from single-view depth scans of real
objects.

Computer Vision and Pattern Recognition