Abstract Waddington’s epigenetic landscape has long served as a conceptual framework for understanding cell fate decisions. The landscape’s geometry encodes the molecular mechanisms that guide the gene expression profiles of uncommitted cells toward terminally differentiated cell types. In this study, we demonstrate that applying the concept of intrinsic dimension to single-cell transcriptomic data can effectively capture trends in expression trajectories, supporting this framework. This approach allows us to define a robust cell potency score without relying on prior biological information. By analyzing an extensive collection of datasets from various species, experimental protocols, and differentiation processes, we validate our method and successfully reproduce established hierarchies of cell type potency. Our work provides a direct link between geometric properties of single-cell expression profiles and the level of differentiation of a cell population.