This article was accepted into 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 score-based generative modeling to these domains, the score network must be carefully designed, making its applicability to arbitrary data domains difficult. In this article we address this problem by taking a \textit{functional} view of data. This functional view allows apparently different domains to be converted into a common shared representation. We then reformulate the scoring 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 in non-Euclidean systems. geometry.
