Understanding factors that cause species' geographic range limits is a major focus in ecology and evolution. The central marginal hypothesis (CMH) predicts that species cannot adapt to conditions beyond current geographic range edges because genetic diversity decreases from core to edge due to smaller, more isolated edge populations. We employed a population genomics framework using 24 235–33 112 SNP loci to test major predictions of the CMH in the ongoing invasion of the cane toad (Rhinella marina) in Australia. Cane toad tissue samples were collected along broad-scale, core-to-edge transects across their invasive range. Geographic and ecological core areas were identified using GIS and habitat suitability indices from ecological niche modelling. Bayesian clustering analyses revealed three genetic clusters, in the northwest invasion-front region, northeast precipitation-limited region and southeast cold temperature-limited region. Core-to-edge patterns of genetic diversity and differentiation were consistent with the CMH in the southeast, but were not supported in the northeast and showed mixed support in the northwest. Results suggest cold temperatures are a likely contributor to southeastern range limits, consistent with CMH predictions. In the northeast and northwest, ecological processes consisting of a steep physiological barrier and ongoing invasion dynamics, respectively, are more likely explanations for population genomic patterns than the CMH.