Generative artificial intelligence (AI) excels at producing complex data structures (text, images, videos) by learning patterns from training examples. Across scientific disciplines, researchers are now applying generative models to "inverse problems" to directly predict hidden parameters from observed data along with measures of uncertainty. While these predictive or posterior-based methods can handle intractable likelihoods and large-scale studies, they can also produce biased or overconfident conclusions even without model misspecifications. We present a solution with Frequentist-Bayes (FreB), a mathematically rigorous protocol that reshapes AI-generated posterior probability distributions into (locally valid) confidence regions that consistently include true parameters with the expected probability, while achieving minimum size when training and target data align. We demonstrate FreB's effectiveness by tackling diverse case studies in the physical sciences: identifying unknown sources under dataset shift, reconciling competing theoretical models, and mitigating selection bias and systematics in observational studies. By providing validity guarantees with interpretable diagnostics, FreB enables trustworthy scientific inference across fields where direct likelihood evaluation remains impossible or prohibitively expensive.

翻译：生成式人工智能（AI）通过从训练样本中学习模式，擅长生成复杂的数据结构（文本、图像、视频）。在各个科学领域，研究人员正将生成模型应用于“逆问题”，以直接从观测数据中预测隐藏参数并量化不确定性。尽管这些基于预测或后验分布的方法能够处理难以处理的似然函数和大规模研究，但即使在模型设定无误的情况下，它们也可能产生有偏或过度自信的结论。我们提出了一种解决方案——频率主义-贝叶斯（FreB）方法，这是一种数学上严谨的协议，可将AI生成的后验概率分布重塑为（局部有效的）置信区域，这些区域能以预期概率一致地包含真实参数，并在训练数据与目标数据一致时达到最小尺寸。我们通过物理科学中的多个案例研究证明了FreB的有效性：在数据集偏移下识别未知源、调和相互竞争的理论模型，以及在观测研究中减轻选择偏差和系统误差。通过提供具有可解释诊断的有效性保证，FreB能够在直接似然评估仍不可能或成本过高的领域实现可靠的科学推断。