Inverse Problem Sampling in Latent Space Using Sequential Monte Carlo

TL;DR

This paper introduces LD-SMC, a novel sequential Monte Carlo method in the latent space of diffusion models, improving inverse image reconstruction tasks like inpainting on datasets such as ImageNet and FFHQ.

Contribution

The paper proposes a new SMC-based sampling approach in the latent space of diffusion models to enhance inverse problem solving in image processing.

Findings

LD-SMC outperforms existing methods in inverse tasks

Significant improvements in challenging inpainting scenarios

Effective in datasets like ImageNet and FFHQ

Abstract

In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that can guide the reconstruction towards solutions that appear natural. The success of diffusion models over the last few years has made them a leading candidate for this task. However, the sequential nature of diffusion models makes this conditional sampling process challenging. Furthermore, since diffusion models are often defined in the latent space of an autoencoder, the encoder-decoder transformations introduce additional difficulties. To address these challenges, we suggest a novel sampling method based on sequential Monte Carlo (SMC) in the latent space of diffusion models. We name our method LD-SMC. We define a generative model for the data using additional auxiliary observations and perform posterior inference with SMC sampling based on a reverse diffusion process. Empirical evaluations on ImageNet and FFHQ show the benefits of LD-SMC over competing methods in various inverse problem tasks and especially in challenging inpainting tasks.