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.

翻译：本文提出一种新方法，用于三维形状的生成、反演与操控，该方法通过对小波域中的连续隐式表示进行直接生成式建模。具体而言，我们提出一种紧凑的小波表示，利用一对粗系数体积与细节系数体积，通过截断符号距离函数与多尺度双正交小波隐式表征三维形状。随后，我们设计了一对神经网络：一个基于扩散的生成器，用于以粗系数体积形式生成多样化的形状；以及一个细节预测器，用于生成兼容的细节系数体积以引入精细结构与细节。此外，我们联合训练一个编码器网络，以学习用于反演形状的潜空间，从而支持丰富的全局形状与区域感知形状操控。定量与定性实验结果均表明，相较于当前最先进方法，我们的方法在形状生成、反演与操控方面展现出显著优势。