This paper presents a new approach for 3D shape generation, enabling direct
generative modeling on a continuous implicit representation in wavelet domain.
Specifically, we propose a compact wavelet representation with a pair of coarse
and detail coefficient volumes to implicitly represent 3D shapes via truncated
signed distance functions and multi-scale biorthogonal wavelets, and formulate
a pair of neural networks: a generator based on the diffusion model to produce
diverse shapes in the form of coarse coefficient volumes; and a detail
predictor to further produce compatible detail coefficient volumes for
enriching the generated shapes with fine structures and details. Both
quantitative and qualitative experimental results manifest the superiority of
our approach in generating diverse and high-quality shapes with complex
topology and structures, clean surfaces, and fine details, exceeding the 3D
generation capabilities of the state-of-the-art models