This paper reviews how a diverse set of popular data-driven priors commonly used in Bayesian inverse problems can be unified through their respective score functions. By framing these priors under this common perspective, we show that they can benefit from their straightfoward and effective integration into a recently proposed sampling algorithm. The applicability of this common framework is illustrated by considering several data-driven priors, namely regularization-by-denoising, normalizing flow-based priors, score-based generative models, and convex-ridge regularizers. For these four particular priors, the performance of the method is evaluated when conducting image inpainting and single image super-resolution. These results, as well as those obtained when restoring real images acquired in a geological context, demonstrate the efficiency of the method. This unified framework proves versatile enough to handle any posterior distribution defined by a broad class of score function-based priors, beyond the specific cases considered in this paper.

翻译：本文综述了贝叶斯逆问题中常用的多种数据驱动先验如何通过各自的得分函数实现统一。通过将这些先验置于这一共同视角下，我们证明它们能够以直接有效的方式集成到近期提出的采样算法中。该统一框架的适用性通过考虑四种数据驱动先验得以阐释：去噪正则化、归一化流先验、基于得分的生成模型以及凸脊正则化器。针对这四种特定先验，我们在图像修复和单图像超分辨率任务中评估了该方法的表现。这些结果，以及在地质背景下恢复真实图像所获得的结果，共同证明了该方法的有效性。这一统一框架被证明足够灵活，能够处理由得分函数先验的广泛类别定义的任意后验分布，其适用范围远超本文所讨论的具体案例。