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表述关于目标信号的先验信念，并精确描述其如何表现为噪声观测。基于稀疏性等手工设计的信号先验正日益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，最先进的基于分数的扩散模型在性能和灵活性方面尤为突出。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的结构化噪声模型。为此，我们提出一种联合条件反向扩散过程，该过程利用针对噪声和信号生成分布的学习分数。我们在多种包含结构化噪声的逆问题中展示了显著的性能提升，优于使用归一化流和对抗网络的竞争基线方法。这为扩散建模在非高斯测量模型逆问题中的应用开辟了新机遇和相关实际应用场景。