Cell fate determination is a continuous process in which one cell type diversifies to other cell types following a hierarchical path. Advancements in single-cell technologies provide the opportunity to reveal the continuum of cell progression which forms a structured continuous tree. Computational algorithms, which are usually based on a priori assumptions on the hidden structures, have previously been proposed as a means of recovering pseudo-trajectory along cell differentiation process. However, there still lack of statistical framework on the assessments of intrinsic structure embedded in high-dimensional gene expression profile. Inherit noise and cell-to-cell variation underlie the single-cell data, on the other hand, pose grand challenges to testing even basic structures, such as linear versus bifurcation.