The loss of sexual recombination and segregation in asexual organisms has been portrayed as an irreversible process that commits asexually reproducing lineages to reduced diversification. We test this hypothesis by estimating rates of speciation, extinction, and transition between sexuality and functional asexuality in the evening primroses. Specifically, we estimate these rates using the recently developed BiSSE (Binary State Speciation and Extinction) phylogenetic comparative method, which employs maximum likelihood and Bayesian techniques. We infer that net diversification rates (speciation minus extinction) in functionally asexual evening primrose lineages are roughly eight times faster than diversification rates in sexual lineages, largely due to higher speciation rates in asexual lineages. We further reject the hypothesis that a loss of recombination and segregation is irreversible because the transition rate from functional asexuality to sexuality is significantly greater than zero and in fact exceeded the reverse rate. These results provide the first empirical evidence in support of the alternative theoretical prediction that asexual populations should instead diversify more rapidly than sexual populations because they are free from the homogenizing effects of sexual recombination and segregation. Although asexual reproduction may often constrain adaptive evolution, our results show that the loss of recombination and segregation need not be an evolutionary dead end in terms of diversification of lineages.