Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency

Fuente: arXiv
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Main Authors: Song, Bowen, Kwon, Soo Min, Zhang, Zecheng, Hu, Xinyu, Qu, Qing, Shen, Liyue
Format: Preprint
Published: 2023
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author Song, Bowen
Kwon, Soo Min
Zhang, Zecheng
Hu, Xinyu
Qu, Qing
Shen, Liyue
author_facet Song, Bowen
Kwon, Soo Min
Zhang, Zecheng
Hu, Xinyu
Qu, Qing
Shen, Liyue
contents Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their applicability as priors for high-dimensional real-world data such as medical images. Latent diffusion models, which operate in a much lower-dimensional space, offer a solution to these challenges. However, incorporating latent diffusion models to solve inverse problems remains a challenging problem due to the nonlinearity of the encoder and decoder. To address these issues, we propose \textit{ReSample}, an algorithm that can solve general inverse problems with pre-trained latent diffusion models. Our algorithm incorporates data consistency by solving an optimization problem during the reverse sampling process, a concept that we term as hard data consistency. Upon solving this optimization problem, we propose a novel resampling scheme to map the measurement-consistent sample back onto the noisy data manifold and theoretically demonstrate its benefits. Lastly, we apply our algorithm to solve a wide range of linear and nonlinear inverse problems in both natural and medical images, demonstrating that our approach outperforms existing state-of-the-art approaches, including those based on pixel-space diffusion models.
format Preprint
id arxiv_https___arxiv_org_abs_2307_08123
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency
Song, Bowen
Kwon, Soo Min
Zhang, Zecheng
Hu, Xinyu
Qu, Qing
Shen, Liyue
Computer Vision and Pattern Recognition
Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their applicability as priors for high-dimensional real-world data such as medical images. Latent diffusion models, which operate in a much lower-dimensional space, offer a solution to these challenges. However, incorporating latent diffusion models to solve inverse problems remains a challenging problem due to the nonlinearity of the encoder and decoder. To address these issues, we propose \textit{ReSample}, an algorithm that can solve general inverse problems with pre-trained latent diffusion models. Our algorithm incorporates data consistency by solving an optimization problem during the reverse sampling process, a concept that we term as hard data consistency. Upon solving this optimization problem, we propose a novel resampling scheme to map the measurement-consistent sample back onto the noisy data manifold and theoretically demonstrate its benefits. Lastly, we apply our algorithm to solve a wide range of linear and nonlinear inverse problems in both natural and medical images, demonstrating that our approach outperforms existing state-of-the-art approaches, including those based on pixel-space diffusion models.
title Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency
topic Computer Vision and Pattern Recognition
url https://arxiv.org/abs/2307.08123