A recent line of research has exploited pre-trained generative diffusion models as priors for solving Bayesian inverse problems. We contribute to this research direction by designing a sequential Monte Carlo method for linear-Gaussian inverse problems which builds on "decoupled diffusion", where the generative process is designed such that larger updates to the sample are possible. The method is asymptotically exact and we demonstrate the effectiveness of our Decoupled Diffusion Sequential Monte Carlo (DDSMC) algorithm on both synthetic as well as protein and image data. Further, we demonstrate how the approach can be extended to discrete data.

翻译：近期一系列研究利用预训练的生成扩散模型作为先验来解决贝叶斯反问题。我们通过设计一种适用于线性高斯反问题的序列蒙特卡洛方法，对该研究方向做出贡献。该方法基于"解耦扩散"技术构建——其生成过程经过专门设计，使得样本能够实现更大程度的更新。该方法具有渐近精确性，我们通过合成数据、蛋白质数据及图像数据验证了解耦扩散序列蒙特卡洛（DDSMC）算法的有效性。此外，我们还展示了该方法如何扩展至离散数据场景。