Infinite-Dimensional Diffusion Models for Function Spaces
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We define diffusion-based generative models in infinite dimensions, and apply them to the generative modeling of functions. By first formulating such models in the infinite-dimensional limit and only then discretizing, we are able to obtain a sampling algorithm that has dimension-free bounds on the distance from the sample measure to the target measure. Furthermore, we propose a new way to perform conditional sampling in an infinite-dimensional space and show that our approach outperforms previously suggested procedures.
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