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SUMMARY:Convergence of Diffusion Models Under the Manifold Hypothesis in H
 igh-Dimensions
DTSTART:20250404T151500
DTEND:20250404T161500
DTSTAMP:20260528T051208Z
UID:3ac0d1529a78cbc1e3571a74d20d4a37e0421fd8d57661228b5db837
CATEGORIES:Conferences - Seminars
DESCRIPTION:Judith Rousseau\, University of Oxford\nDenoising Diffusion Pr
 obabilistic Models (DDPM) are powerful state-of-the-art methods used to ge
 nerate synthetic data from high-dimensional data distributions and are wid
 ely used for image\, audio and video generation as well as many more appli
 cations in science and beyond. The \\textit{manifold hypothesis} states th
 at high-dimensional data often lie on lower-dimensional manifolds within a
 n ambient space of large dimension D\, and is widely believed to hold in p
 rovided examples. While recent results have provided invaluable insight in
 to how diffusion models adapt to the manifold hypothesis\, they do not cap
 ture the great empirical success of these models.\nIn this work\, we study
  DDPMs under the manifold hypothesis and prove that they achieve rates ind
 ependent of the ambient dimension in terms of learning the score. In terms
  of sampling\, we obtain rates independent of the ambient dimension w.r.t.
  the Kullback-Leibler divergence\, and $O(\\sqrt{D})$ w.r.t. the Wasserste
 in distance. We do this by developing a new framework connecting diffusion
  models to the well-studied theory of extrema of Gaussian Processes.\nThis
  is a joint work with I. Azangulov and  G. Deligliannidis (Univ of Oxford
 )
LOCATION:CM 1 517 https://plan.epfl.ch/?room==CM%201%20517
STATUS:CONFIRMED
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