Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models
Main Conference Track
Authors: Litu Rout, Negin Raoof, Giannis Daras, Constantine Caramanis, Alex Dimakis, Sanjay Shakkottai

We present the first framework to solve linear inverse problems leveraging pre-trained \textit{latent} diffusion models.  Previously proposed algorithms (such as DPS and DDRM) only apply to \textit{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.