Mode Collapse Is Cheap to Detect: A Ground-Truth-Free Pre-Flight Check for Neural Samplers

Neural samplers are trained against an unnormalised target $\tilde{\pi }=e^{-E}$ with no samples from $\pi$, so a practitioner cannot tell whether an expensive run has silently dropped part of the target. The usual diagnostics are expectations under the model and are therefore confined to its support: we exhibit a sampler with self-normalised $\mathrm{ESS}=0.99$ that misses $87\%$ of the mass. Splitting the missing mass into lost support and misallocated weight shows the two established diagnostic families have disjoint blind spots – ESS is blind to the first, and normaliser comparison is provably blind to the second at any budget, returning $0.0000$ while up to $64\%$ of the mass is misallocated. We then argue that detecting missing mass is easier than sampling it – detection needs one point per missed basin plus local curvature, while correcting the sampler generally costs substantially more – and turn this into a pre-flight check using only $E,\nabla E,{\nabla }^{2}E$. On exactly solvable targets the check reaches $10^{-3}$-level accuracy at a few percent of training cost on the harder benchmarks, while a tuned SMC reference requires $70$–$280\%$ of training cost, and it applies unchanged to a controlled-SDE sampler with no tractable density. A self-diagnostic flags configurations whose estimate should not be believed, but cannot certify a run: a mode with attraction probability below $1/R$ escapes the estimator and the diagnostic together. We map the resulting boundary on LJ-13.