Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo
This work provides an incremental improvement for researchers in computational statistics and machine learning by enhancing sampling efficiency in linear-Gaussian inverse problems.
The paper tackles Bayesian inverse problems by introducing a sequential Monte Carlo method based on decoupled diffusion, which allows larger sample updates and is asymptotically exact. The method is demonstrated on synthetic, protein, and image data, showing effectiveness and extension to discrete data.
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.