PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers

TL;DR - PosteriorBench evaluates whether generative inverse solvers recover complete posterior distributions rather than merely producing plausible point estimates. It exposes significant distribution-matching and uncertainty-calibration gaps across current methods.

• Covers four physics-based tasks: Darcy flow, Poisson source recovery, carbon storage, and light-transport material inference.
• Uses high-fidelity reference posteriors generated through established methods such as rejection sampling and Markov chain Monte Carlo.
• Measures posterior statistics, distributional alignment, and frequency fidelity with five complementary metrics.
• Experiments indicate that neural operators improve robustness across resolutions, while guidance weights and generation noise strongly affect posterior-variance calibration.