The development of a phenotype in a multicellular organism often involves multiple, simultaneously occurring biological processes. Advances in single-cell RNA-sequencing make it possible to infer latent developmental processes from the transcriptomic profiles of cells at various developmental stages. Accurate characterization is challenging however, particularly for periodic processes such as cell cycle. To address this, we develop Cyclum, an autoencoder approach identifying circular trajectories in the gene expression space. Cyclum substantially improves the accuracy and robustness of cell-cycle characterization beyond existing approaches. Applying Cyclum to removing cell-cycle effects substantially improves delineations of cell subpopulations, which is useful for establishing various cell atlases and studying tumor heterogeneity.