Summary Existing computational methods that use single-cell RNA-sequencing for cell fate prediction either summarize observations of cell states and their couplings without modeling the underlying differentiation process, or are limited in their capacity to model complex differentiation landscapes. Thus, contemporary methods cannot predict how cells evolve stochastically and in physical time from an arbitrary starting expression state, nor can they model the cell fate consequences of gene expression perturbations. We introduce PRESCIENT (Potential eneRgy undErlying Single Cell gradIENTs), a generative modeling framework that learns an underlying differentiation landscape from single-cell time-series gene expression data. Our generative model framework provides insight into the process of differentiation and can simulate differentiation trajectories for arbitrary gene expression progenitor states. We validate our method on a recently published experimental lineage tracing dataset that provides observed trajectories. We show that this model is able to predict the fate biases of progenitor cells in neutrophil/macrophage lineages when accounting for cell proliferation, improving upon the best-performing existing method. We also show how a model can predict trajectories for cells not found in the model’s training set, including cells in which genes or sets of genes have been perturbed. PRESCIENT is able to accommodate complex perturbations of multiple genes, at different time points and from different starting cell populations. PRESCIENT models are able to recover the expected effects of known modulators of cell fate in hematopoiesis and pancreatic β cell differentiation.