Xin Ju

This work introduces PosteriorBench, a benchmark for evaluating the distributional accuracy of generative inverse solvers, and reveals substantial distribution-matching gaps across current solvers, while showing that neural operators improve resolution robustness, and guidance weights and generation noise are key to posterior-variance calibration.

Diffusion models can now solve notoriously ill-posed inverse problems in carbon capture and storage, outperforming standard methods by an order of magnitude and even rivaling asymptotically exact methods like Rejection Sampling, but with better physical realism.