Reconstructing the biogeographic history of groups present in continuous arid landscapes is challenging dueto the difficulties in defining discrete areas for analyses, and even more so when species largely overlap both in terms ofgeography and habitat preference. In this study, we use a novel approach to estimate ancestral areas for the small plantgenus Centipeda. We apply continuous diffusion of geography by a relaxed random walk where each species is sampledfrom its extant distribution on an empirical distribution of time-calibrated species-trees. Using a distribution of previouslypublished substitution rates of the internal transcribed spacer (ITS) for Asteraceae, we show how the evolution of Centipedacorrelates with the temporal increase of aridity in the arid zone since the Pliocene. Geographic estimates of ancestral speciesshow a consistent pattern of speciation of early lineages in the Lake Eyre region, with a division in more northerly andsoutherly 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 GreatVictoria Desert, the Gibson Desert, and the Great Sandy Desert, or beyond the main continental shelf of Australia. Theresult indicates all western occurrences of the genus to be a result of recent dispersal rather than ancient vicariance. Thisstudy contributes to our understanding of the spatiotemporal processes shaping the flora of the arid zone, and offers asignificant improvement in inference of ancestral areas for any organismal group distributed where it remains difficult todescribe geography in terms of discrete areas.