We propose a probabilistic model for estimating population flow, which is defined as populations of the transition between areas over time, given aggregated spatio-temporal population data. Since there is no information about individual trajectories in the aggregated data, it is not straightforward to estimate population flow. With the proposed method, we utilize a collective graphical model with which we can learn individual transition models from the aggregated data by analytically marginalizing the individual locations. Learning a spatio-temporal collective graphical model only from the aggregated data is an ill-posed problem since the number of parameters to be estimated exceeds the number of observations. The proposed method reduces the effective number of parameters by modeling the transition probabilities with a neural network that takes the locations of the origin and the destination areas and the time of day as inputs. By this modeling, we can automatically learn nonlinear spatio-temporal relationships flexibly among transitions, locations, and times. With four real-world population data sets in Japan and China, we demonstrate that the proposed method can estimate the transition population more accurately than existing methods.