PosteriorBench: going beyond point reconstructions for scientific inverse-problem to full posterior distributions. Many scientific problems involve indirect or partial observations. Multiple physical fields can explain the same measurements. A solver should capture these possibilities, yet reconstruction accuracy alone is misleading. We spent substantial compute to construct high-fidelity reference posteriors across four tasks: Darcy flow inversion, Poisson source recovery, carbon capture and storage, and light transport material inference. These reference data let researchers directly evaluate their solvers using five complementary metrics. One of our key findings: better reconstruction accuracy can coincide with worse posterior recovery. Even strong generative samplers struggle to get both the mean and variance right, often underestimating the uncertainty. Paper: Code: Thanks to Jiachen Yao, Sean Hsu, Xi Deng, and all our coauthors for making this work possible @Caltech #AIforScience# #InverseProblems# #UncertaintyQuantification#