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

Research Scientific Inverse Problems

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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.

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

arXiv cs.LG Jiachen Yao, Zi-Siang Hsu, Xi Deng, Aditi Gupta, Xin Ju, Sally M Benson, Gege Wen, Anima Anandkumar 2026-09-17 arXiv:2609.20794
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Providers: Hugging Face · N/A OpenAlex · N/A Publisher · N/A Semantic Scholar · N/A X · N/A Fetched 2026-09-26 14:15:10.326443 UTC

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.
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