  This paper presents a new approach for 3D shape generation, inversion, and
manipulation, through a 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. Then, we design a pair of neural networks: a
diffusion-based generator to produce diverse shapes in the form of the coarse
coefficient volumes and a detail predictor to produce compatible detail
coefficient volumes for introducing fine structures and details. Further, we
may jointly train an encoder network to learn a latent space for inverting
shapes, allowing us to enable a rich variety of whole-shape and region-aware
shape manipulations. Both quantitative and qualitative experimental results
manifest the compelling shape generation, inversion, and manipulation
capabilities of our approach over the state-of-the-art methods.
