Diffusion probabilistic models have quickly become a major approach for generative modeling of images, 3D geometry, video and other domains. However, to adapt diffusion generative modeling to these domains the denoising network needs to be carefully designed for each domain independently, oftentimes under the assumption that data lives in a Euclidean grid. In this paper we introduce Diffusion Probabilistic Fields (DPF), a diffusion model that can learn distributions over continuous functions defined over metric spaces, commonly known as fields. We extend the formulation of diffusion probabilistic models to deal with this field parametrization in an explicit way, enabling us to define an end-to-end learning algorithm that side-steps the requirement of representing fields with latent vectors as in previous approaches (Dupont et al., 2022a; Du et al., 2021). We empirically show that, while using the same denoising network, DPF effectively deals with different modalities like 2D images and 3D geometry, in addition to modeling distributions over fields defined on non-Euclidean metric spaces.

翻译：扩散概率模型已迅速成为图像、三维几何、视频及其他领域生成建模的主要方法。然而，为将这些扩散生成模型适配至这些领域，去噪网络需针对每个领域独立精心设计，且通常假设数据存在于欧几里得网格中。本文提出扩散概率场（DPF），这是一种扩散模型，能够学习定义在度量空间上的连续函数（通常称为场）的分布。我们扩展了扩散概率模型的公式，以显式方式处理这种场的参数化，从而定义了一种端到端学习算法，避免了先前方法（Dupont et al., 2022a；Du et al., 2021）中使用隐向量表示场的要求。实验表明，在采用相同去噪网络的情况下，DPF 能有效处理二维图像和三维几何等不同模态，此外还能对定义在非欧几里得度量空间上的场进行分布建模。