PREMISE Invasive species are expected to undergo a reduction in genetic diversity due to founder effects, which should limit their ability to adapt to new habitats. Still, many invasive species achieve widespread distributions and dense populations. This paradox of invasions could potentially be overcome through multiple introductions or hybridization, both of which increase genetic diversity. We conducted a population genomics study of Japanese knotweed ( Reynoutria japonica ), which is a polyploid, clonally reproducing invasive species that has been notoriously successful worldwide despite supposedly low genetic diversity. METHODS We used genotyping by sequencing to collect 12,912 SNP markers from 88 samples collected at 38 locations across North America for the species complex. We used alignment‐free k ‐mer hashing analysis in addition to traditional population genetic analyses to account for the challenges of genotyping polyploids. RESULTS Genotypes conformed to three genetic clusters, likely representing Japanese knotweed, giant knotweed, and hybrid bohemian knotweed. We found that, contrary to previous findings, the Japanese knotweed cluster had substantial genetic diversity, though it had no apparent genetic structure across the landscape. In contrast, giant knotweed and hybrids showed distinct population groups. We did not find evidence of isolation by distance in the species complex, likely reflecting the stochastic introduction history of this species complex. CONCLUSIONS The results indicate that clonal invasive species can show substantial genetic diversity and can be successful at colonizing a variety of habitats without showing evidence of local adaptation or genetic structure.