PosteriorBench: A Benchmark for Evaluating Posterior Matching in Generative Inverse Problem Solvers

Forum topic · 小凯 · 2026-09-19

Summary

PosteriorBench (arXiv:2609.20794) is a benchmark for evaluating the distributional accuracy of generative models used to solve scientific inverse problems. Existing evaluations focus on whether a method produces a single plausible reconstruction, which is insufficient for ill-posed problems where multiple solutions may be consistent with the same sparse or noisy observations. A solver can achieve strong pointwise accuracy while failing to capture the true posterior via mode collapse, overconfident uncertainty, or averaging incompatible solutions. PosteriorBench evaluates four physics-based inverse problems: Darcy flow inversion, Poisson source recovery, carbon capture and storage, and light transport material inference. For each task, high-fidelity reference posteriors are constructed using established but computationally expensive methods such as rejection sampling and Markov chain Monte Carlo. The benchmark pairs these references with a five-metric posterior evaluation suite: posterior mean error, posterior standard deviation error, maximum mean discrepancy, sliced Wasserstein distance, and radially averaged power spectrum error. Experiments reveal significant distribution-matching gaps in current solvers, while showing that neural operators improve resolution robustness, and that guidance weights and generation noise are key to posterior variance calibration.

Overview

Research area: Machine Learning Authors: Jiachen Yao, Zi-Siang Hsu, Xi Deng, Aditi Gupta, Xin Ju, Sally M Benson, Gege Wen, Anima Anandkumar arXiv: 2609.20794

Generative models are increasingly used to solve scientific inverse problems, but existing evaluations still focus primarily on whether a method can produce a single plausible reconstruction. This is insufficient for ill-posed problems, where multiple solutions may be consistent with the same sparse or noisy observations. In these settings, a method can achieve strong pointwise accuracy while still failing to capture the true posterior through mode collapse, overconfident uncertainty, or averaging incompatible solutions.

Key contributions

PosteriorBench, a benchmark for evaluating the distributional accuracy of generative inverse solvers, covering four physics-based inverse problems:
Darcy flow inversion
Poisson source recovery
Carbon capture and storage
Light transport material inference
For each task, high-fidelity reference posteriors are constructed using computationally expensive but established procedures (e.g., rejection sampling and Markov chain Monte Carlo), enabling direct evaluation of whether a solver recovers the full solution set rather than a single best sample.
A five-metric posterior evaluation suite:
Posterior mean error
Posterior standard deviation error
Maximum mean discrepancy (MMD)
Sliced Wasserstein distance
Radially averaged power spectrum error

These metrics assess pointwise accuracy, marginal uncertainty, distributional alignment, and global frequency fidelity. The benchmark covers sparse sensing, low-resolution observations, nonlinear forward models, varying noise levels, and multimodal priors, and provides a unified pipeline for distribution matching and uncertainty quantification.

Findings

Experiments reveal significant distribution-matching gaps in current solvers. Neural operators improve robustness to resolution changes, while guidance weights and generation noise are critical factors for posterior variance calibration.

*Source: zhichai.net, auto-collected 2026-09-19.*