The history of insects' taxonomic diversity is poorly understood. The two most common methods for estimating taxonomic diversity in deep time yield conflicting results: the 'range through' method suggests a steady, nearly monotonic increase in family-level diversity, whereas 'shareholder quorum subsampling' suggests a highly volatile taxonomic history with family-level mass extinctions occurring repeatedly, even at the midpoints of geological periods. The only feature shared by these two diversity curves is a steep increase in standing diversity during the Early Cretaceous. This apparent diversification event occurs primarily during the Aptian, the pre-Cenozoic interval with the most described insect occurrences, raising the possibility that this feature of the diversity curves reflects preservation and sampling biases rather than insect evolution and extinction. Here, the capture-mark-recapture (CMR) approach is used to estimate insects' family-level diversity. This method accounts for the incompleteness of the insect fossil record as well as uneven sampling among time intervals. The CMR diversity curve shows extinctions at the Permian/Triassic and Cretaceous/Palaeogene boundaries but does not contain any mass extinctions within geological periods. This curve also includes a steep increase in diversity during the Aptian, which appears not to be an artefact of sampling or preservation bias because this increase still appears when time bins are standardized by the number of occurrences they contain rather than by the amount of time that they span. The Early Cretaceous increase in family-level diversity predates the rise of angiosperms by many millions of years and can be better attributed to the diversification of parasitic and especially parasitoid insect lineages.