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SUMMARY:Non-asymptotic bounds for forward processes in denoising diffusion
 s: Ornstein-Uhlenbeck is optimal - Aleksandar Mijatovic (University of War
 wick)\, Miha Bresar (University of Warwick)
DTSTART:20240701T093000Z
DTEND:20240701T110000Z
UID:TALK218356@talks.cam.ac.uk
DESCRIPTION:Denoising diffusion probabilistic models (DDPMs) represent a r
 ecent advance in generative modelling that has delivered state-of-the-art 
 results across many domains of applications. Despite their success\, a rig
 orous theoretical understanding of the error within these generative model
 s\, particularly the non-asymptotic bounds for the forward diffusion proce
 sses\, remain scarce. Making minimal assumptions on the initial data distr
 ibution\, allowing for example the manifold hypothesis\, this paper presen
 ts explicit non-asymptotic bounds on the forward diffusion error in total 
 variation (TV)\, expressed as a function of &nbsp\;the terminal time $T$. 
 We parametrize an arbitrary data distribution in terms of the maximal dist
 ance $R$ between its modes and consider forward diffusions with additive a
 nd multiplicative noise. Our analysis rigorously proves that\, under mild 
 assumptions\, the canonical choice of the Ornstein-Uhlenbeck (OU) process 
 cannot be significantly improved in terms of reducing the terminal time $T
 $ as a function $R$ and &nbsp\;error tolerance $\\eps>0$. We also establis
 h a cut-off like phenomenon (as $R\\to\\infty$) for the convergence of an 
 OU process to its invariant measure in TV\, initialized at a multi-modal d
 istribution with maximal mode distance $R$\, typically present in DDPMs.
LOCATION:External
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