When Does Conditional Vendi Measure Posterior Diversity?

Conditional generation requires separating diversity within a condition from variation across conditions. We characterise the discrepancy between averaged conditional kernel entropy and joint-minus-conditioning entropy. For a finite condition catalogue, we obtain an attainable certificate determined by the conditioning kernel, an exact equality criterion, and sharp recovery limits when only the aggregate score is retained. Global spectral truncation creates a second obstruction: even with orthogonal condition features, its rank budget can erase or reverse conditional diversity. A conditional tail decomposition retains an explicit approximation bound. Exact controls isolate these mechanisms, and an audit of 1,200 released images finds 31 native-generator ranking reversals across 112 kernel and subset specifications. The initial correction certifies none of these reversals, while a post hoc refinement certifies all on the same banks. A prospective Qwen3 study with 4,096 stochastic outputs certifies a finite-bank temperature ordering, with no native ranking reversal. Population entropy rankings remain unresolved. The analysis identifies which conclusions aggregate scores support and gives an evaluation protocol based on direct grouping, explicit compression error and sampling uncertainty.