Existing RNA velocity estimation methods strongly rely on predefined dynamics and cell-agnostic constant transcriptional kinetic rates, assumptions often violated in complex and heterogeneous single-cell RNA sequencing (scRNA-seq) data. Using a graph convolution network, DeepVelo overcomes these limitations by generalizing RNA velocity to cell populations containing time-dependent kinetics and multiple lineages. DeepVelo infers time-varying cellular rates of transcription, splicing, and degradation, recovers each cell's stage in the differentiation process, and detects functionally relevant driver genes regulating these processes. Application to various developmental and pathogenic processes demonstrates DeepVelo's capacity to study complex differentiation and lineage decision events in heterogeneous scRNA-seq data.