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Modern methods for counting people in crowded scenes rely on deep networks to estimate people densities in individual images. As such, only very few take advantage of temporal consistency in video sequences, and those that do only impose weak smoothness constraints across consecutive frames. In this paper, we advocate estimating people flows across image locations between consecutive images and inferring the people densities from these flows instead of directly regressing them. This enables us to impose much stronger constraints encoding the conservation of the number of people. As a result, it significantly boosts performance without requiring a more complex architecture. Furthermore, it allows us to exploit the correlation between people flow and optical flow to further improve the results. We also show that leveraging people conservation constraints in both a spatial and temporal manner makes it possible to train a deep crowd counting model in an active learning setting with much fewer annotations. This significantly reduces the annotation cost while still leading to similar performance to the full supervision case.