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.

本文通过对小波域中的连续隐式表示进行直接生成建模，提出了一种 3D 形状生成、反演和操作的新方法。具体来说，我们提出了一种紧凑的小波表示，具有一对粗略和细节系数体积，通过截断符号距离函数和多尺度双正交小波隐式表示 3D 形状。然后，我们设计了一对神经网络：一个基于扩散的生成器，以粗略系数体积的形式生成各种形状，以及一个细节预测器，以生成兼容的细节系数体积以引入精细结构和细节。此外，我们可以联合训练编码器网络来学习反转形状的潜在空间，从而使我们能够实现丰富多样的整体形状和区域感知形状操作。定量和定性实验结果都表明，我们的方法相对于最先进的方法具有令人信服的形状生成、反转和操纵能力。