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SUMMARY:Provably Robust Score-Based Diffusion Posterior Sampling for Plug-
 and-Play Image Reconstruction - Yuejie  Chi (Carnegie Mellon University)
DTSTART:20240719T090000Z
DTEND:20240719T100000Z
UID:TALK219067@talks.cam.ac.uk
DESCRIPTION:In a great number of tasks in science and engineering\, the go
 al is to infer an unknown image from a small number of noisy measurements 
 collected from a known forward model describing certain sensing or imaging
  modality. Due to resource constraints\, this image reconstruction task is
  often extremely ill-posed\, which necessitates the adoption of expressive
  prior information to regularize the solution space. Score-based diffusion
  models\, thanks to its impressive empirical success\, have emerged as an 
 appealing candidate of an expressive prior in image reconstruction. In ord
 er to accommodate diverse tasks at once\, it is of great interest to devel
 op efficient\, consistent and robust algorithms that incorporate unconditi
 onal score functions of an image prior distribution in conjunction with fl
 exible choices of forward models. This work develops an algorithmic framew
 ork for employing score-based diffusion models as an expressive data prior
  in nonlinear inverse problems with general forward models. Motivated by t
 he plug-and-play framework in the imaging community\, we introduce a diffu
 sion plug-and-play method (DPnP) that alternatively calls two samplers\, a
  proximal consistency sampler based solely on the likelihood function of t
 he forward model\, and a denoising diffusion sampler based solely on the s
 core functions of the image prior. The key insight is that denoising under
  white Gaussian noise can be solved rigorously via both stochastic (i.e.\,
  DDPM-type) and deterministic (i.e.\, DDIM-type) samplers using the same s
 et of score functions trained for generation. We establish both asymptotic
  and non-asymptotic performance guarantees of DPnP\, and provide numerical
  experiments to illustrate its promise in solving both linear and nonlinea
 r image reconstruction tasks. To the best of our knowledge\, DPnP is the f
 irst provably-robust posterior sampling method for nonlinear inverse probl
 ems using unconditional diffusion priors.&nbsp\;
LOCATION:External
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