Infinite-Dimensional Diffusion Models

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• Jakiw Pidstrigach (University of Oxford)
• Tuesday 16 July 2024, 13:30-14:30
• External.

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DMLW01 - International workshop on diffusions in machine learning: foundations, generative models, and optimisation

Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standard approach is first to discretize and then to apply diffusion models to the discretized data. We instead directly formulate diffusion-based generative models in infinite dimensions and apply them to the generative modelling of functions. We prove that our formulations are well posed in the infinite-dimensional setting and provide dimension-independent distance bounds from the sample to the target measure. Using our theory, we also develop guidelines for the design of infinite-dimensional diffusion models. For image distributions, these guidelines are in line with current canonical choices.

This talk is part of the Isaac Newton Institute Seminar Series series.

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