Paper ID: 2307.00619

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.

Submitted: Jul 2, 2023