Manifold Diffusion Fields

This paper was accepted at the Diffusion Models workshop at NeurIPS 2023.

Score-based models have quickly become the de facto choice for generative modeling of images, text and more recently molecules. However, to adapt a score-based generative modeling to these domains the score network needs to be carefully designed, hampering its applicability to arbitrary data domains. In this paper we tackle this problem by taking a \textit{functional} view of data. This functional view allows to cast seemingly different domains to a common shared representation. We then re-formulate the score function to deal with functional data and show: i) this unified architecture can be effectively applied to different modalities: images, geometry, video, and ii) we can learn generative models of signals defined on non-euclidean geometry.