Solving Linear Inverse Problems Provably via Posterior Sampling with
  Latent Diffusion Models
Litu Rout Negin Raoof Giannis Daras Constantine Caramanis Alexandros G. Dimakis Sanjay Shakkottai
We present the first framework to solve linear inverse problems leveraging
pre-trained latent diffusion models. Previously proposed algorithms (such as
DPS and DDRM) only apply to pixel-space diffusion models. We theoretically
analyze our algorithm showing provable sample recovery in a linear model
setting. The algorithmic insight obtained from our analysis extends to more
general settings often considered in practice. Experimentally, we outperform
previously proposed posterior sampling algorithms in a wide variety of problems
including random inpainting, block inpainting, denoising, deblurring,
destriping, and super-resolution.