Flatworms of the species Schmidtea mediterranea are immortal-adult animals contain a large pool of pluripotent stem cells that continuously differentiate into all adult cell types. Therefore, single-cell transcriptome profiling of adult animals should reveal mature and progenitor cells. By combining perturbation experiments, gene expression analysis, a computational method that predicts future cell states from transcriptional changes, and a lineage reconstruction method, we placed all major cell types onto a single lineage tree that connects all cells to a single stem cell compartment. We characterized gene expression changes during differentiation and discovered cell types important for regeneration. Our results demonstrate the importance of single-cell transcriptome analysis for mapping and reconstructing fundamental processes of developmental and regenerative biology at high resolution.