<p>Time-series spatial transcriptomics with single-cell resolution provides an opportunity to study cell differentiation, proliferation and migration in physical space over time. However, because sequencing is destructive, reconstructing spatiotemporal dynamics from snapshots remains challenging. In particular, inferring migration is difficult because samples collected at different time points often lie in different coordinate systems across biological replicates. Here we show that spatiotemporal video cassette recorder (stVCR), a generative deep-learning framework, can reconstruct continuous cell differentiation, proliferation, physical-space migration and spatial alignment in an end-to-end manner. The model integrates dynamical optimal transport in an unbalanced setting, density matching that is invariant to rigid transformations, and biologically informed priors to preserve spatial structure. stVCR also enables interpretable analysis of how phenotype transitions interact with spatial migration and proliferation. Using both simulated and real datasets, we demonstrate that stVCR is effective and robust, and we apply it to uncover spatiotemporal dynamics in axolotl brain regeneration and 3D <i>Drosophila</i> embryo development.</p>