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UID:DSC-23000
DTSTART;TZID=Europe/Berlin:20260626T140000
SEQUENCE:1782452367
TRANSP:OPAQUE
DTEND;TZID=Europe/Berlin:20260626T150000
URL:https://dresden-science-calendar.de/calendar/en/detail/23000
LOCATION:MPI-PKS\, Nöthnitzer Straße 3801187 Dresden
SUMMARY:Chertkov: Path Integral Diffusion: From Integrable Bridge to Adapti
 ve\, Guided\, and Mean-Field Sampling
CLASS:PUBLIC
DESCRIPTION:Speaker: Prof. Michael Chertkov\nInstitute of Speaker: Universi
 ty of Arizona\nTopics:\nPhysik\n Location:\n  Name: MPI-PKS ()\n  Street: 
 Nöthnitzer Straße 38\n  City: 01187 Dresden\n  Phone: + 49 (0)351 871 0\
 n  Fax: \nDescription: Diffusion models of Generative AI are usually intro
 duced through learned score fields and reverse-time stochastic dynamics. I
 n this talk\, I will present an alternative\, control-theoretic viewpoint 
 in which generative sampling is formulated as a bridge-diffusion problem a
 nd solved through Path Integral Diffusion (PID). In this framework\, sampl
 ing is recast as stochastic optimal transport with potential\, and the opt
 imal drift admits an explicit representation through forward and backward 
 Green functions. For harmonic potentials\, this yields an analytic and int
 erpretable construction in which the score\, drift\, and predicted termina
 l state can all be written in closed form.  I will then discuss two natura
 l extensions. First\, in Adaptive PID\, the quadratic stiffness of the pot
 ential is allowed to vary in time. With piecewise-constant schedules and G
 aussian-mixture targets\, the resulting bridge remains analytically tracta
 ble\, making it possible to optimize transient behavior rather than only t
 erminal accuracy. This leads to a new perspective on quality of sampling i
 n terms of pathwise diagnostics such as sensitivity of the drift. Second\,
  in Guided PID\, the center of the quadratic potential is also allowed to 
 move\, providing a mechanism to steer flows in probability space and\, in 
 some applications\, in physical space as well.  These constructions lead n
 aturally to Mean-Field PID\, where samples no longer evolve independently 
 but interact through a self-consistent mean field. This produces a coopera
 tive version of bridge diffusion\, connecting generative modeling with McK
 ean–Vlasov dynamics and mean-field control. The overall message is that 
 one can move from standard diffusion sampling to adaptive\, guided\, and u
 ltimately cooperative sampling while preserving a large degree of analytic
  control and interpretability.   Dr. Michael \"Misha\" Chertkov is a Profe
 ssor of Mathematics and Chair of the Graduate Interdisciplinary Program in
  Applied Mathematics at the University of Arizona. His research addresses 
 foundational challenges in mathematics\, statistics\, machine learning\, a
 nd artificial intelligence\, particularly as they apply to and are inspire
 d by physical systems like fluid mechanics. He also works on applications 
 in the control of engineered systems\, such as energy grids\, and bio-soci
 al systems. Dr. Chertkov received his Ph.D. in physics from the Weizmann I
 nstitute of Science in 1996. After obtaining his Ph.D.\, he spent three ye
 ars as a R.H. Dicke Fellow in the Department of Physics at Princeton Unive
 rsity. In 1999\, he joined the Los Alamos National Laboratory\, first as a
  J.R. Oppenheimer Fellow\, later becoming a Technical Staff Member in the 
 Theory Division. He transitioned to the University of Arizona in 2019. Thr
 oughout his career\, Dr. Chertkov has contributed about 300 research paper
 s. He holds the title of Fellow in both the AAAS and the American Physical
  Society and is a Senior Member of IEEE.
DTSTAMP:20260626T222354Z
CREATED:20260620T053919Z
LAST-MODIFIED:20260626T053927Z
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