  The Gaussian diffusion model, initially designed for image generation, has
recently been adapted for 3D point cloud generation. However, these adaptations
have not fully considered the intrinsic geometric characteristics of 3D shapes,
thereby constraining the diffusion model's potential for 3D shape manipulation.
To address this limitation, we introduce a novel deformable 3D shape diffusion
model that facilitates comprehensive 3D shape manipulation, including point
cloud generation, mesh deformation, and facial animation. Our approach
innovatively incorporates a differential deformation kernel, which deconstructs
the generation of geometric structures into successive non-rigid deformation
stages. By leveraging a probabilistic diffusion model to simulate this
step-by-step process, our method provides a versatile and efficient solution
for a wide range of applications, spanning from graphics rendering to facial
expression animation. Empirical evidence highlights the effectiveness of our
approach, demonstrating state-of-the-art performance in point cloud generation
and competitive results in mesh deformation. Additionally, extensive visual
demonstrations reveal the significant potential of our approach for practical
applications. Our method presents a unique pathway for advancing 3D shape
manipulation and unlocking new opportunities in the realm of virtual reality.
