Understanding cell state transitions and their governing regulatory mechanisms remains one of the fundamental questions in biology. We develop a computational method, state transition inference using cross-cell correlations (STICCC), for predicting reversible and irreversible cell state transitions at single-cell resolution by using gene expression data and a set of gene regulatory interactions. The method is inspired by the fact that the gene expression time delays between regulators and targets can be exploited to infer past and future gene expression states. From applications to both simulated and experimental single-cell gene expression data, we show that STICCC-inferred vector fields capture basins of attraction and irreversible fluxes. By connecting regulatory information with systems' dynamical behaviors, STICCC reveals how network interactions influence reversible and irreversible state transitions. Compared to existing methods that infer pseudotime and RNA velocity, STICCC provides complementary insights into the gene regulation of cell state transitions.