Probabilistic diffusion models have achieved state-of-the-art results for image synthesis, inpainting, and text-to-image tasks. However, they are still in the early stages of generating complex 3D shapes. This work proposes Diffusion-SDF, a generative model for shape completion, single-view reconstruction, and reconstruction of real-scanned point clouds. We use neural signed distance functions (SDFs) as our 3D representation to parameterize the geometry of various signals (e.g., point clouds, 2D images) through neural networks. Neural SDFs are implicit functions and diffusing them amounts to learning the reversal of their neural network weights, which we solve using a custom modulation module. Extensive experiments show that our method is capable of both realistic unconditional generation and conditional generation from partial inputs. This work expands the domain of diffusion models from learning 2D, explicit representations, to 3D, implicit representations.

翻译：概率扩散模型在图像合成、修复及文本到图像任务中已取得最先进成果，但在复杂三维形状生成领域仍处于早期阶段。本文提出Diffusion-SDF——一种用于形状补全、单视角重建及真实扫描点云重建的生成模型。我们采用神经符号距离函数（SDF）作为三维表征，通过神经网络参数化各类信号（如点云、二维图像）的几何特性。神经SDF属于隐式函数，对其扩散相当于学习其网络权重的逆向过程，我们通过定制调制模块解决该问题。大量实验表明，本方法不仅能实现逼真的无条件生成，还能基于不完整输入完成条件生成。该工作将扩散模型的研究范畴从二维显式表征扩展至三维隐式表征。