Recent diffusion models provide a promising zero-shot solution to noisy
linear inverse problems without retraining for specific inverse problems. In
this paper, we propose the first unified interpretation for existing zero-shot
methods from the perspective of approximating the conditional posterior mean
for the reverse diffusion process of conditional sampling. We reveal that
recent methods are equivalent to making isotropic Gaussian approximations to
intractable posterior distributions over clean images given diffused noisy
images, with the only difference in the handcrafted design of isotropic
posterior covariances. Inspired by this finding, we propose a general
plug-and-play posterior covariance optimization based on maximum likelihood
estimation to improve recent methods. To achieve optimal posterior covariance
without retraining, we provide general solutions based on two approaches
specifically designed to leverage pre-trained models with and without reverse
covariances. Experimental results demonstrate that the proposed methods
significantly enhance the overall performance or robustness to hyperparameters
of recent methods. Code is available at
this https URL

最新的扩散模型为嘈杂的线性反问题提供了一种无需为特定反问题重新训练的有希望的零样本解决方案。本文首次从条件抽样的逆扩散过程的条件后验均值的近似角度解释了现有的零照片方法。我们揭示了最新方法相当于对给定扩散嘈杂图像的干净图像的不可行后验分布进行各向同性高斯近似，唯一的不同在于各向同性后验协方差的手工设计。受此发现的启发，我们提出了一种基于最大似然估计的通用即插即用后验协方差优化方法，以改善最新方法。为了实现无需重新训练的最优后验协方差，我们提供了基于两种方法的通用解决方案，这两种方法专门设计用于利用具有和不具有逆协方差的预训练模型。实验结果表明，所提出的方法显著提高了最新方法的整体性能或对超参数的鲁棒性。可在此链接获取代码。