In this talk we introduce a mathematical model to describe temporal processes like embryonic development and cellular reprogramming. We consider stochastic processes in gene expression space to represent developing populations of cells, and we use optimal transport to recover the temporal couplings of the process. We apply these ideas to study 315,000 single-cell RNA-sequencing profiles collected at 40 time points over 18 days of reprogramming fibroblasts into induced pluripotent stem cells. To validate the optimal transport model, we demonstrate that it can accurately predict developmental states at held-out time points. We construct a high-resolution map of reprogramming that rediscovers known features; uncovers new alternative cell fates including neural- and placental-like cells; predicts the origin and fate of any cell class; and implicates regulatory models in particular trajectories. Of these findings, we highlight the transcription factor Obox6 and the paracrine signaling factor GDF9, which we experimentally show enhance reprogramming efficiency. Our approach provides a general framework for investigating cellular differentiation, and poses some interesting theoretical questions.