Pre-trained diffusion models have been successfully used as priors in a variety of linear inverse problems, where the goal is to reconstruct a signal from noisy linear measurements. However, existing approaches require knowledge of the linear operator. In this paper, we propose GibbsDDRM, an extension of Denoising Diffusion Restoration Models (DDRM) to a blind setting in which the linear measurement operator is unknown. GibbsDDRM constructs a joint distribution of the data, measurements, and linear operator by using a pre-trained diffusion model for the data prior, and it solves the problem by posterior sampling with an efficient variant of a Gibbs sampler. The proposed method is problem-agnostic, meaning that a pre-trained diffusion model can be applied to various inverse problems without fine tuning. In experiments, it achieved high performance on both blind image deblurring and vocal dereverberation tasks, despite the use of simple generic priors for the underlying linear operators.

翻译：预训练的扩散模型已成功用作多种线性逆问题的先验，其目标是从含噪线性测量中重建信号。然而，现有方法需要知晓线性算子。本文提出GibbsDDRM，将去噪扩散修复模型（DDRM）扩展至线性测量算子未知的盲设置。GibbsDDRM通过利用数据先验的预训练扩散模型，构建数据、测量和线性算子的联合分布，并采用吉布斯采样器的高效变体进行后验采样以求解问题。所提方法具有问题无关性，即预训练扩散模型无需微调即可应用于多种逆问题。实验表明，尽管对底层线性算子采用简单通用先验，该方法在盲图像去模糊和语音去混响任务中均实现了高性能。