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Manifold Diffusion Fields

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…