An important question in early neural development is the origin of stochastic nuclear movement between apical and basal surfaces of neuroepithelia during interkinetic nuclear migration. Tracking of nuclear subpopulations has shown evidence of diffusion - mean squared displacements growing linearly in time - and suggested crowding from cell division at the apical surface drives basalward motion. Yet, this hypothesis has not yet been tested, and the forces involved not quantified. We employ long-term, rapid light-sheet and two-photon imaging of early zebrafish retinogenesis to track entire populations of nuclei within the tissue. The time-varying concentration profiles show clear evidence of crowding as nuclei reach close-packing and are quantitatively described by a nonlinear diffusion model. Considerations of nuclear motion constrained inside the enveloping cell membrane show that concentration-dependent stochastic forces inside cells, compatible in magnitude to those found in cytoskeletal transport, can explain the observed magnitude of the diffusion constant.