The introduction of RNA velocity in single cells has opened up new ways of studying cellular differentiation. The originally proposed framework obtains velocities as the deviation of the observed ratio of spliced and unspliced mRNA from an inferred steady state. Errors in velocity estimates arise if the central assumptions of a common splicing rate and the observation of the full splicing dynamics with steady-state mRNA levels are violated. With scVelo (https://scvelo.org), we address these restrictions by solving the full transcriptional dynamics of splicing kinetics using a likelihood-based dynamical model. This generalizes RNA velocity to a wide variety of systems comprising transient cell states, which are common in development and in response to perturbations. We infer gene-specific rates of transcription, splicing and degradation, and recover the latent time of the underlying cellular processes. This latent time represents the cell’s internal clock and is based only on its transcriptional dynamics. Moreover, scVelo allows us to identify regimes of regulatory changes such as stages of cell fate commitment and, therein, systematically detects putative driver genes. We demonstrate that scVelo enables disentangling heterogeneous subpopulation kinetics with unprecedented resolution in hippocampal dentate gyrus neurogenesis and pancreatic endocrinogenesis. We anticipate that scVelo will greatly facilitate the study of lineage decisions, gene regulation, and pathway activity identification.