For more than a decade there has been interdisciplinary debate on whether fossil origination and extinction time series show evidence of self-organized criticality (SOC) or some other, more complex hierarchical structure. Analyses of a new data set of Jurassic and Cretaceous ammonoid genera demonstrate that these taxonomic subgroups do not reproduce the patterns seen in larger data sets that pool disparate taxa. Rather, originations and extinctions in these ammonoids show no evidence of SOC, limited evidence for a hierarchical multifractal pattern, and, at least within the suborder Ammonitina, evidence consistent with a white noise signal. Although a white noise pattern has been identified previously in an ammonoid family diversity time series, the significance of such a result for ammonoid genus originations and extinctions is discussed here for the first time. This white noise pattern indicates that processes acting on short time scales (less than a few million years) dominate the Ammonitina origination and extinction records, producing a nonhierarchical diversity dynamic. Because origination events in one interval do not appear to trigger originations in subsequent intervals, ammonite evolutionary radiations were likely to be extremely rapid and driven by physical rather than biological opportunities for diversification.