We propose a new model of internal migration, based on persistent and spatially-correlated idiosyncratic utility. The model is motivated by a new fact in the data that simple moving cost models struggle to match: the t-year interstate migration rate is proportional to the square root of t. The new model maintains the tractability and flexibility of standard migration models, but better matches the dynamics of migration, including the new fact. It has substantially different welfare implications and makes different counterfactual predictions, especially in terms of dynamic adjustment and long-run responses.