Cell differentiation is steered by extracellular signals that activate a cell type specific transcriptional program. Molecular mechanisms that drive the differentiation can be analyzed by combining mathematical modeling with population average data. For standard mathematical models, the population average data is informative only if the measurements come from a homogeneous cell culture. In practice, however, the differentiation efficiencies are always imperfect. Consequently, cell cultures are inherently mixtures of several cell types, which have different molecular mechanisms and exhibit quantitatively different dynamics. There is an urgent need for data-driven mathematical modeling approaches that can detect possible heterogeneity and, further, recover the molecular mechanisms from heterogeneous data.