Palaeobiodiversity analysis underpins macroevolutionary investigations, allowing identification of mass extinctions and adaptive radiations. However, recent large-scale studies on marine invertebrates indicate that geological factors play a central role in moulding the shape of diversity curves and imply that many features of such curves represent sampling artefacts, rather than genuine evolutionary events. In order to test whether similar biases affect diversity estimates for terrestrial taxa, we compiled genus-richness estimates for three Mesozoic dinosaur clades (Ornithischia, Sauropodomorpha and Theropoda). Linear models of expected genus richness were constructed for each clade, using the number of dinosaur-bearing formations available through time as a proxy for the amount of fossiliferous rock outcrop. Modelled diversity estimates were then compared with observed patterns. Strong statistically robust correlations demonstrate that almost all aspects of ornithischian and theropod diversity curves can be explained by geological megabiases, whereas the sauropodomorph record diverges from modelled predictions and may be a stronger contender for identifying evolutionary signals. In contrast to other recent studies, we identify a marked decline in dinosaur genus richness during the closing stages of the Cretaceous Period, indicating that the clade decreased in diversity for several million years prior to the final extinction of non-avian dinosaurs at the Cretaceous-Palaeocene boundary.