Recent studies of ancient genomes have suggested that gene flow from archaic hominin groups to the ancestors of modern humans occurred on two separate occasions during the modern human expansion out of Africa. At the same time, decreasing levels of human genetic diversity have been found at increasing distance from Africa as a consequence of human expansion out of Africa. We analyzed the signal of archaic ancestry in modern human populations, and we investigated how serial founder models of human expansion affect the signal of archaic ancestry using simulations. For descendants of an archaic admixture event, we show that genetic drift coupled with ascertainment bias for common alleles can cause artificial but largely predictable differences in similarity to archaic genomes. In genotype data from non-Africans, this effect results in a biased genetic similarity to Neandertals with increasing distance from Africa. However, in addition to the previously reported gene flow between Neandertals and non-Africans as well as gene flow between an archaic human population from Siberia ("Denisovans") and Oceanians, we found a significant affinity between East Asians, particularly Southeast Asians, and the Denisova genome-a pattern that is not expected under a model of solely Neandertal admixture in the ancestry of East Asians. These results suggest admixture between Denisovans or a Denisova-related population and the ancestors of East Asians, and that the history of anatomically modern and archaic humans might be more complex than previously proposed.