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SUMMARY:LC2 Seminar – Matías Delgadino (University of Texas at Austin)
DESCRIPTION:Title: Diffusion-based Posterior Sampling: A Feynman-Kac Analys
 is of Bias and Stability\nAbstract: Diffusion-based posterior samplers us
 e pretrained diffusion priors to sample from measurement- or reward-condit
 ioned posteriors\, and are widely used for inverse problems. Yet their the
 oretical behavior remains poorly understood: even with exact prior scores\
 , their outputs are biased\, and in low-temperature regimes their discreti
 zations can become unstable. We characterize this bias by introducing a tr
 actable surrogate path connecting the true posterior to a standard Gaussia
 n and comparing it to the sampler’s path. Their density ratio satisfies 
 a parabolic PDE whose reaction term measures the accumulated bias. A Feynm
 an-Kac representation then expresses the Radon-Nikodym correction as an ex
 plicit path expectation\, identifying which posterior regions are over- or
  under-sampled.\n\nWe apply this framework to DPS and STSL\, a related sam
 pler. For DPS\, the correction is an Ornstein-Uhlenbeck path expectation c
 oupling the data conditional covariance with the reward curvature\, reveal
 ing where DPS over- or under-samples. Next\, we reinterpret STSL as an aux
 iliary drift that steers trajectories toward low-uncertainty regions\, fla
 ttening the spatially varying part of the DPS reaction term. Finally\, we 
 characterize early guidance-stopping\, a common mitigation for low-tempera
 ture instabilities caused by forward-Euler integration of the vector field
 . Together\, these results clarify sampler bias\, explain existing correct
 ives\, and guide stable variant designs.
URL:https://www.imperial.ac.uk/events/209771/lc2-seminar-matias-delgadino-u
 niversity-of-texas-at-austin/
DTSTART;TZID=Europe/London:20260527T130000
DTEND;TZID=Europe/London:20260527T140000
LOCATION:140\, Huxley Building\, South Kensington Campus\, Imperial College
  London\, London\, SW7 2AZ\, United Kingdom
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