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.

本文提出了一种基于连续小波嵌入式表示的3D形状生成、反演、操纵方法，包括紧凑的小波表示、扩散生成器、细节预测器、编码器等，实现了较为强大的形状生成、反演、操纵能力，优于现有的最新方法。

神经小波扩散用于3D形状生成、反转和操作