Diffusion Probabilistic Fields

TL;DR

This paper introduces Diffusion Probabilistic Fields (DPF), a novel diffusion model capable of learning distributions over continuous functions across various domains and metric spaces, simplifying adaptation across modalities.

Contribution

The paper presents DPF, a diffusion model that directly learns over fields without latent vectors, enabling flexible application to Euclidean and non-Euclidean spaces.

Findings

Effective across 2D images and 3D geometry

Handles non-Euclidean metric spaces

Eliminates need for domain-specific denoising networks

Abstract

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.