Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models

TL;DR

This paper introduces a novel framework that uses pre-trained latent diffusion models for solving linear inverse problems, providing theoretical guarantees and outperforming existing methods across various applications.

Contribution

It is the first to leverage pre-trained latent diffusion models for linear inverse problems with provable recovery guarantees, extending previous pixel-space methods.

Findings

The proposed algorithm achieves provable sample recovery in linear models.

It outperforms existing posterior sampling algorithms in diverse inverse problems.

The approach generalizes to practical settings beyond the linear model assumption.

Abstract

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.