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SUMMARY:Local Diffusion Models and Phases of Data Distributions [Confirmed
 ]
DTSTART:20260204T160000Z
DTEND:20260204T173000Z
DTSTAMP:20260419T013300Z
UID:indico-event-400@events.perimeterinstitute.ca
DESCRIPTION:Speakers: Xun Gao (University of Colorado\, Boulder)\n\nAs a c
 lass of generative artificial intelligence frameworks inspired by statisti
 cal physics\, diffusion models have shown extraordinary performance in syn
 thesizing complicated data distributions through a denoising process gradu
 ally guided by score functions. Real-life data\, like images\, is often sp
 atially structured in low-dimensional spaces. However\, ordinary diffusion
  models ignore this local structure and learn spatially global score funct
 ions\, which are often computationally expensive. In this work\, motivated
  by recent advances in statistical physics\, we develop a generic framewor
 k for defining phases of data distributions and use it to analyze the loca
 lity requirements of denoisers in diffusion models. We define two distribu
 tions as belonging to the same data distribution phase if they can be mutu
 ally connected via spatially local operations such as local denoisers. We 
 demonstrate that the reverse denoising process consists of an early trivia
 l phase and a late data phase\, sandwiching a rapid phase transition where
  local denoisers must fail. We further demonstrate that the performance of
  local denoisers is closely tied to spatial Markovianity\, which provides 
 an operational criterion for diagnosing such phase transitions. We validat
 e this criterion through numerical experiments on real-world datasets. Our
  work suggests guidance for simpler and more efficient architectures of di
 ffusion models: far from the phase transition point\, we can use small loc
 al neural networks to compute the score function\; global neural networks 
 are only necessary around the narrow time interval of phase transitions. T
 his result also opens up new directions for studying phases of data distri
 butions\, the broader science of generative artificial intelligence\, and 
 guiding the design of neural networks inspired by physics concepts.\n\nhtt
 ps://events.perimeterinstitute.ca/event/400/
LOCATION:PI/4-405 - Bob Room (Perimeter Institute for Theoretical Physics)
URL:https://events.perimeterinstitute.ca/event/400/
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