Beyond Accuracy: Diagnosing Flow Matching Posterior Estimation through Endpoint Variability

Flow matching posterior estimation (FMPE) offers a flexible and increasingly important approach to simulation-based Bayesian inference, enabling expressive posterior approximation through learned continuous-time transport. Yet its performance can be difficult to diagnose through conventional posterior-accuracy metrics, as they cannot reliably distinguish expected sample-size-driven variability from systematic errors induced by suboptimal configurations. In this work, we develop a theoretically grounded diagnostic based on the $N^{-1/2}$ scaling of endpoint variability across training-set sizes. Building on the predicted scaling law, we construct a statistical test for assessing whether the sample-size-driven behavior of FMPE is consistent with theoretical expectations, and develop a pseudo-dataset strategy that reduces the need for extensive repeated simulator runs. Experiments, including domain-specific evaluations with complex epidemiological simulators, support the validity of our proposed diagnostic and show that it can identify suboptimal FMPE configurations.