Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are increasingly replaced by data-driven deep generative models, and several groups have recently shown that state-of-the-art score-based diffusion models yield particularly strong performance and flexibility. In this paper, we show that the powerful paradigm of posterior sampling with diffusion models can be extended to include rich, structured, noise models. To that end, we propose a joint conditional reverse diffusion process with learned scores for the noise and signal-generating distribution. We demonstrate strong performance gains across various inverse problems with structured noise, outperforming competitive baselines that use normalizing flows and adversarial networks. This opens up new opportunities and relevant practical applications of diffusion modeling for inverse problems in the context of non-Gaussian measurement models.

翻译：解决病态逆问题需要仔细构建关于目标信号的先验信念，并精确描述其如何表现为含噪测量值。基于稀疏性等手工艺设计的信号先验正逐渐被数据驱动的深度生成模型所取代，近期多个研究团队已证明，基于得分的先进扩散模型展现出尤为强大的性能与灵活性。本文表明，基于扩散模型的后验采样这一强大范式可扩展至包含丰富、结构化的噪声模型。为此，我们提出了一种联合条件反向扩散过程，该过程利用学习到的噪声与信号生成分布的得分函数。我们在多种带有结构化噪声的逆问题上展现出显著的性能提升，超越了使用归一化流和对抗网络的竞争性基线方法。这为扩散模型在非高斯测量模型背景下的逆问题研究开辟了新机遇与重要的实际应用场景。