Diffusion probabilistic fashions have rapidly turn into a significant method for generative modeling of photos, 3D geometry, video and different domains. Nonetheless, to adapt diffusion generative modeling to those domains the denoising community must be fastidiously designed for every area independently, oftentimes beneath the belief that information lives in an Euclidean grid. On this paper we introduce Diffusion Probabilistic Fields (DPF), a diffusion mannequin that may be taught distributions over steady features outlined over metric areas, generally referred to as fields. We lengthen the formulation of diffusion probabilistic fashions to cope with this subject parametrization in an specific manner, enabling us to outline and end-to-end studying algorithm that side-steps the requirement of representing fields with latent vectors as in earlier approaches. We empirically present that, whereas utilizing the identical denoising community, DPF successfully offers with totally different modalities like 2D photos and 3D geometry, along with modeling distributions over fields outlined on non-Euclidean metric areas.