Real-time spatiotemporal population data is attracting a great deal of attention for understanding crowd movements in cities.The data is the aggregation of personal location information and consists of just areas and the number of people in each area at certain time instants. Accordingly, it does not explicitly represent crowd movement. This paper proposes a probabilistic model based on collective graphical models that can estimate crowd movement from spatiotemporal population data. There are two technical challenges: (i) poor estimation accuracy as the traditional approach means the model would have too many degrees of freedom, (ii) excessive computation cost. Our key idea for overcoming these two difficulties is to model the transition probability between grid cells (cells hereafter) in a geospatial grid space by using three factors: departure probability of cells, gathering score of cells, and geographical distance between cells. These advances enable us to reduce the degrees of freedom of the model appropriately and derive an efficient estimation algorithm.  To evaluate the performance of our method, we conduct experiments using real-world spatiotemporal population data. The results confirm the effectiveness of our method, both in estimation accuracy and computation cost.