Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo

Previous methods for posterior sampling A recent line of research has exploited pre-trained generative with diffusion priors, while providing impressive diffusion models as priors for solving Bayesian results on tasks like image reconstruction (Kawar et al., inverse problems. We contribute to this research direction 2022; Chung et al., 2023; Song et al., 2023), often rely by designing a sequential Monte Carlo method on approximations and fail or perform poorly on simple for linear-Gaussian inverse problems which builds on tasks (Cardoso et al., 2024, and our Section 5.1), "decoupled diffusion", where the generative process is making it uncertain to what extent they can solve designed such that larger updates to the sample are Bayesian inference problems in general.