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

TL;DR

PosteriorBench introduces a comprehensive benchmark for evaluating generative inverse solvers by assessing their ability to match full posterior distributions, not just point estimates. It uses high-fidelity reference posteriors from MCMC and rejection sampling across four physics-based inverse problems and evaluates solvers with five metrics targeting distributional accuracy, uncertainty calibration, and spectral fidelity.

Why It Matters

Many scientific inverse problems involve ambiguous or multimodal solutions, where accurate uncertainty quantification is critical. Current evaluation methods fail to detect poor posterior coverage, leading to overconfident or incorrect conclusions. PosteriorBench enables more reliable model selection and trust in generative solvers for real-world applications.

Key Findings

• Existing generative inverse solvers exhibit significant gaps in distributional accuracy despite strong pointwise performance.
• Neural operators demonstrate improved robustness to low-resolution and sparse observations.
• Guidance weights and generation noise play crucial roles in calibrating posterior variance and avoiding overconfidence.