Stem cells have received much attention recently for their potential utility in regenerative medicine. The identification of their differentiated progeny often requires complex staining procedures, and is challenging for intermediary stages which are a priori unknown. In this work, the ability of label-free quantitative coherent anti-Stokes Raman scattering (CARS) micro-spectroscopy to identify populations of intermediate cell states during the differentiation of murine embryonic stem cells into adipocytes is assessed. Cells were imaged at different days of differentiation by hyperspectral CARS, and images were analysed with an unsupervised factorization algorithm providing Raman-like spectra and spatially resolved maps of chemical components. Chemical decomposition combined with a statistical analysis of their spatial distributions provided a set of parameters that were used for classification analysis. The first 2 principal components of these parameters indicated 3 main groups, attributed to undifferentiated cells, cells differentiated into committed white pre-adipocytes, and differentiating cells exhibiting a distinct protein globular structure with adjacent lipid droplets. An unsupervised classification methodology was developed, separating undifferentiated cell from cells in other stages, using a novel method to estimate the optimal number of clusters. The proposed unsupervised classification pipeline of hyperspectral CARS data offers a promising new tool for automated cell sorting in lineage analysis.