Trustworthy Scientific Inference for Inverse Problems with Generative Models

Music City Center 

Across scientific disciplines, researchers increasingly use generative AI to approach ``inverse problems'' (inferring hidden parameters from observed data). Although these methods bypass intractable likelihoods and reduce computational costs, they can produce misleading conclusions through biased and/or overconfident parameter estimates. We present Frequentist-Bayes (FreB), a protocol that transforms AI-generated probability distributions into rigorous confidence regions that consistently include true parameters with the expected probability while remaining precise when training and target data align. We demonstrate FreB's effectiveness by tackling diverse case studies in the physical sciences: identifying unknown sources under domain shift, reconciling competing theoretical models, and mitigating selection effects in observational studies. By providing validity guarantees without sacrificing efficiency, FreB enables trustworthy scientific inference and uncertainty quantification across fields where direct likelihood evaluation remains impossible or prohibitively expensive.