Pretrained diffusion models (DMs) have recently been popularly used in solving inverse problems (IPs). The existing methods mostly interleave iterative steps in the reverse diffusion process and iterative steps to bring the iterates closer to satisfying the measurement constraint. However, such interleaving methods struggle to produce final results that look like natural objects of interest (i.e., manifold feasibility) and fit the measurement (i.e., measurement feasibility), especially for nonlinear IPs. Moreover, their capabilities to deal with noisy IPs with unknown types and levels of measurement noise are unknown. In this paper, we advocate viewing the reverse process in DMs as a function and propose a novel plug-in method for solving IPs using pretrained DMs, dubbed DMPlug. DMPlug addresses the issues of manifold feasibility and measurement feasibility in a principled manner, and also shows great potential for being robust to unknown types and levels of noise. Through extensive experiments across various IP tasks, including two linear and three nonlinear IPs, we demonstrate that DMPlug consistently outperforms state-of-the-art methods, often by large margins especially for nonlinear IPs. The code is available at https://github.com/sun-umn/DMPlug.

翻译：预训练的扩散模型（DMs）近来被广泛应用于求解逆问题（IPs）。现有方法大多在反向扩散过程的迭代步骤与促使迭代结果满足测量约束的迭代步骤之间进行交错。然而，此类交错方法难以生成既看起来像感兴趣的自然对象（即流形可行性）又符合测量数据（即测量可行性）的最终结果，对于非线性逆问题尤其如此。此外，它们处理具有未知类型和水平测量噪声的含噪逆问题的能力尚不明确。在本文中，我们主张将DMs中的反向过程视为一个函数，并提出一种使用预训练DMs求解逆问题的新颖插件方法，命名为DMPlug。DMPlug以原理性的方式解决了流形可行性和测量可行性问题，并且在应对未知类型和水平的噪声方面展现出巨大潜力。通过对包括两个线性和三个非线性逆问题在内的多种逆任务进行广泛实验，我们证明DMPlug始终优于现有最先进方法，且通常优势显著，尤其对于非线性逆问题。代码可在 https://github.com/sun-umn/DMPlug 获取。