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

PosteriorBench is a benchmark designed to evaluate generative models solving scientific inverse problems. Existing evaluation methods primarily assess whether a single plausible reconstruction can be produced, which is insufficient for ill-posed problems where multiple solutions may be consistent with sparse or noisy observations. The benchmark focuses on posterior matching rather than pointwise accuracy, addressing issues such as mode collapse and overconfident uncertainty estimates that can lead to strong pointwise performance while still failing to capture true posterior distributions.