Conditional generative models became a very powerful tool to sample from Bayesian inverse problem posteriors. It is well-known in classical Bayesian literature that posterior measures are quite robust with respect to perturbations of both the prior measure and the negative log-likelihood, which includes perturbations of the observations. However, to the best of our knowledge, the robustness of conditional generative models with respect to perturbations of the observations has not been investigated yet. In this paper, we prove for the first time that appropriately learned conditional generative models provide robust results for single observations.

翻译：条件生成模型已成为从贝叶斯逆问题后验分布中采样的强大工具。经典贝叶斯文献表明，后验测度对先验测度和负对数似然（包括观测扰动）的扰动具有相当的鲁棒性。然而，据我们所知，条件生成模型关于观测扰动的鲁棒性尚未得到研究。本文首次证明了适当学习的条件生成模型能为单个观测提供鲁棒的结果。