Conditional generative models have become the tool of choice for sampling posteriors in scientific inverse problems, where we seek to sample images or signals conditioned on a set of indirect and noisy measurements. Yet they are often overconfident, which is a critical failure in scientific applications where accurate uncertainty quantification is essential. Existing regularizers fall short in complementary ways: differentiable coverage objectives require the model's density and do not identify the posterior, while strictly proper scoring rules such as the energy score need only samples but do not directly enforce coverage. We close this gap by introducing a differentiable loss function based on the expected coverage probability, estimated from samples alone. It applies to any conditional generative model, with no need for tractable densities or architectural changes. We prove that it is a strict divergence, vanishing if and only if the model equals the true posterior. On simulation-based inference benchmarks, it matches a density-based coverage loss without evaluating the density. On high-dimensional imaging inverse problems, it yields better-calibrated posteriors than scoring-rule regularizers, with little change in the reconstruction quality of point estimates.

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