Changes in transcriptional profiles are at the heart of development. Understanding transcriptional dynamics at the single-cell level is a central challenge in deciphering developmental processes. Current sequencing technologies allow the estimation of transcription profiles at unprecedented single-cell resolution but the inference of developmental progressions of cells is hampered by sampling sparsity, technological noise, and loss of spatial and temporal information. I use noise-resilient diffusion mapping-based approaches to infer and recapitulate developmental trajectories from large single-cell datasets. Our new methods allow us to reconstruct multiple branching trajectories that occur on substantially different timescales in development and infer waves of gene expression changes along the developmental progressions. We analyze the development of vascular cell types, i.e., sieve elements, companion cells, and vessel elements, in different plant organs. We recover known regulators of vascular development that follow expected developmental dynamics based on previous studies and identify putative regulatory factors. We identify waves of gene expression changes of transcription factors and their downstream targets, which provide substantial resolution of transcriptional dynamics in vascular cell development.