a, Development can be modeled as the temporal progression of a population density in transcriptome (cell state) space. Here, the developmental process is a branched lineage from a progenitor to two terminal fates. b, Dimension reductions of the full cell state space are useful for dynamic modelling. Discrete cell types, such as from FACS gates, were previously used for ordinary differential equation models. Branched trajectories with pseudotime coordinates can be used in the context of pseudodynamics. c, Conceptual overview of the pseudodynamics algorithm. The input consists of developmental progress data (normalized distributions across cell state) and population size data (number of cells) for each time point. The output contains interpretable parameter estimates and imputed samples at unseen time points (dotted densities). d, Diffusion map of mouse embryonic stem cell development in vitro after leukemia inhibitory factor (LIF) removal1. Color: days after LIF removal in cell culture. e,f, Kernel density estimate and simulated density of cells across cell state coordinate (diffusion pseudotime) at four sampled time points (n0 = 933, n2 = 303, n4 = 683, n7 = 798 cells) for regularized (ρ = 1) and unregularized (ρ = 0) model fits. Colored density: kernel density estimate, solid line: simulated density based on model fitted to all data, dotted line: simulated density in leave-one-time-point-out cross-validation.