The Unseen-Mode Problem: Certifying Coverage Failures in Molecular Generators

Boltzmann generators are often judged by overlap with a reference ensemble, but high overlap can conceal large errors in metastable-state populations. On the released Sequential Boltzmann Generator for chignolin, recall is $0.987$–$1.000$ and precision is $0.97$, yet a basin holding $28.20\%$ of the reference receives only $0.17\%$ of the samples. We give an exact one-sided lower confidence bound on a basin's probability deficit against a fixed reference. For chignolin it certifies at least a $27.99$ percentage-point deficit and $3.22$ kcal/mol of free-energy error. The same calculation finds deficits in 16 of 17 BioEmu diffusion systems and all 30 Robin autoregressive systems; fresh samples confirm the reported cases, and Robin's reweighting does not remove the four tested deficits. A locally trained 2D alanine-dipeptide flow never samples C7ax, giving at least $357\times$ underweighting against an independent population estimate. We prove that generated samples cannot identify target mass in basins the generator never visits, and that target-directed search has the same limit for basins it never reaches. The certificate therefore measures deficits against an explicit reference.