Reconstructing the biogeographic history of groups present in continuous arid landscapes is challenging due to the difficulties in defining discrete areas for analyses, and even more so when species largely overlap both in terms of geography and habitat preference. In this study, we use a novel approach to estimate ancestral areas for the small plant genus Centipeda. We apply continuous diffusion of geography by a relaxed random walk where each species is sampled from its extant distribution on an empirical distribution of time-calibrated species-trees. Using a distribution of previously published substitution rates of the internal transcribed spacer (ITS) for Asteraceae, we show how the evolution of Centipeda correlates with the temporal increase of aridity in the arid zone since the Pliocene. Geographic estimates of ancestral species show a consistent pattern of speciation of early lineages in the Lake Eyre region, with a division in more northerly and southerly groups since ∼840 ka. Summarizing the geographic slices of species-trees at the time of the latest speciation event (∼20 ka), indicates no presence of the genus in Australia west of the combined desert belt of the Nullabor Plain, the Great Victoria Desert, the Gibson Desert, and the Great Sandy Desert, or beyond the main continental shelf of Australia. The result indicates all western occurrences of the genus to be a result of recent dispersal rather than ancient vicariance. This study contributes to our understanding of the spatiotemporal processes shaping the flora of the arid zone, and offers a significant improvement in inference of ancestral areas for any organismal group distributed where it remains difficult to describe geography in terms of discrete areas.