Diffusion probabilistic models have quickly become an important approach for generative modeling of images, 3D geometry, video, and other domains. However, to fit the generative diffusion model to these domains, the denoising network must be carefully designed for each domain independently, often under the assumption that the data lives on a Euclidean grid. In this article we present 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 probabilistic diffusion models to deal with this field parameterization explicitly, allowing us to define an end-to-end learning algorithm that circumvents the requirement to represent fields with latent vectors as in previous approaches. We show empirically that, using the same denoising network, DPF effectively deals with different modalities such as 2D images and 3D geometry, as well as modeling distributions over fields defined in non-Euclidean metric spaces.
