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.
@article{arxiv.2307.00619,
title = {Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models},
author = {Litu Rout and Negin Raoof and Giannis Daras and Constantine Caramanis and Alexandros G. Dimakis and Sanjay Shakkottai},
journal= {arXiv preprint arXiv:2307.00619},
year = {2023}
}