Inferring cellular trajectories using a variety of omic data is a critical task in single-cell data science. However, accurate prediction of cell fates, and thereby biologically meaningful discovery, is challenged by the sheer size of single-cell data, the diversity of omic data types, and the complexity of their topologies. We present VIA, a scalable trajectory inference algorithm that overcomes these limitations by using lazy-teleporting random walks to accurately reconstruct complex cellular trajectories beyond tree-like pathways (e.g., cyclic or disconnected structures). We show that VIA robustly and efficiently unravels the fine-grained sub-trajectories in a 1.3-million-cell transcriptomic mouse atlas without losing the global connectivity at such a high cell count. We further apply VIA to discovering elusive lineages and less populous cell fates missed by other methods across a variety of data types, including single-cell proteomic, epigenomic, multi-omics datasets, and a new in-house single-cell morphological dataset.