Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance

Fuente: arXiv
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Auteurs principaux: Peng, Xinyu, Zheng, Ziyang, Dai, Wenrui, Xiao, Nuoqian, Li, Chenglin, Zou, Junni, Xiong, Hongkai
Format: Preprint
Publié: 2024
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author Peng, Xinyu
Zheng, Ziyang
Dai, Wenrui
Xiao, Nuoqian
Li, Chenglin
Zou, Junni
Xiong, Hongkai
author_facet Peng, Xinyu
Zheng, Ziyang
Dai, Wenrui
Xiao, Nuoqian
Li, Chenglin
Zou, Junni
Xiong, Hongkai
contents Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we reveal that recent methods can be uniformly interpreted as employing a Gaussian approximation with hand-crafted isotropic covariance for the intractable denoising posterior to approximate the conditional posterior mean. Inspired by this finding, we propose to improve recent methods by using more principled covariance determined by maximum likelihood estimation. To achieve posterior covariance optimization without retraining, we provide general plug-and-play solutions based on two approaches specifically designed for leveraging pre-trained models with and without reverse covariance. We further propose a scalable method for learning posterior covariance prediction based on representation with orthonormal basis. Experimental results demonstrate that the proposed methods significantly enhance reconstruction performance without requiring hyperparameter tuning.
format Preprint
id arxiv_https___arxiv_org_abs_2402_02149
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance
Peng, Xinyu
Zheng, Ziyang
Dai, Wenrui
Xiao, Nuoqian
Li, Chenglin
Zou, Junni
Xiong, Hongkai
Computer Vision and Pattern Recognition
Machine Learning
Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we reveal that recent methods can be uniformly interpreted as employing a Gaussian approximation with hand-crafted isotropic covariance for the intractable denoising posterior to approximate the conditional posterior mean. Inspired by this finding, we propose to improve recent methods by using more principled covariance determined by maximum likelihood estimation. To achieve posterior covariance optimization without retraining, we provide general plug-and-play solutions based on two approaches specifically designed for leveraging pre-trained models with and without reverse covariance. We further propose a scalable method for learning posterior covariance prediction based on representation with orthonormal basis. Experimental results demonstrate that the proposed methods significantly enhance reconstruction performance without requiring hyperparameter tuning.
title Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance
topic Computer Vision and Pattern Recognition
Machine Learning
url https://arxiv.org/abs/2402.02149