Analyzing people flows is important for better navigation and location-based advertising. Since the location information of people is often aggregated for protecting privacy, it is not straightforward to estimate transition populations between locations from aggregated data. Here, aggregated data are incoming and outgoing people counts at each location; they do not contain tracking information of individuals. This paper proposes a probabilistic model for estimating unobserved transition populations between locations from only aggregated data. With the proposed model, temporal dynamics of people flows are assumed to be probabilistic diffusion processes over a network, where nodes are locations and edges are paths between locations. By maximizing the likelihood with flow conservation constraints that incorporate travel duration distributions between locations, our model can robustly estimate transition populations between locations. The statistically significant improvement of our model is demonstrated using real-world datasets of pedestrian data in exhibition halls, bike trip data and taxi trip data in New York City.