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Many recent works in simulation-based inference (SBI) rely on deep generativemodels to approximate complex, high-dimensional posterior distributions.However, evaluating whether or not these approximations can be trusted remainsa challenge. Most approaches evaluate the posterior estimator only inexpectation over the observation space. This limits their interpretability andis not sufficient to identify for which observations the approximation can betrusted or should be improved. Building upon the well-known classifiertwo-sample test (C2ST), we introduce L-C2ST, a new method that allows for alocal evaluation of the posterior estimator at any given observation. It offerstheoretically grounded and easy to interpret -- e.g. graphical -- diagnostics,and unlike C2ST, does not require access to samples from the true posterior. Inthe case of normalizing flow-based posterior estimators, L-C2ST can bespecialized to offer better statistical power, while being computationally moreefficient. On standard SBI benchmarks, L-C2ST provides comparable results toC2ST and outperforms alternative local approaches such as coverage tests basedon highest predictive density (HPD). We further highlight the importance oflocal evaluation and the benefit of interpretability of L-C2ST on a challengingapplication from computational neuroscience.

L-C2ST: Local Diagnostics for Posterior Approximations in Simulation-Based Inference