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SUMMARY:Infinite-Dimensional Diffusion Models - Jakiw Pidstrigach (Univers
 ity of Oxford)
DTSTART:20240716T123000Z
DTEND:20240716T133000Z
UID:TALK219037@talks.cam.ac.uk
DESCRIPTION:Diffusion models have had a profound impact on many applicatio
 n areas\, including those where data are intrinsically infinite-dimensiona
 l\, such as images or time series. The standard approach is first to discr
 etize and then to apply diffusion models to the discretized data. We inste
 ad directly formulate diffusion-based generative models in infinite dimens
 ions and apply them to the generative modelling of functions. We prove tha
 t our formulations are well posed in the infinite-dimensional setting and 
 provide dimension-independent distance bounds from the sample to the targe
 t measure. Using our theory\, we also develop guidelines for the design of
  infinite-dimensional diffusion models. For image distributions\, these gu
 idelines are in line with current canonical choices.
LOCATION:External
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