Imitation learning learns how to act by observing the behavior of an expert demonstrator. We are concerned with a setting where the demonstrations comprise only a subset of state-action pairs (as opposed to the whole trajectories). Our setup reflects the limitations of real-world problems when accessing the expert data. For example, user logs may contain incomplete traces of behavior, or in robotics non-technical human demonstrators may describe trajectories using only a subset of all state-action pairs. A recent approach to imitation learning via distribution matching, ValueDice, tends to overfit when demonstrations are temporally sparse. We counter the overfitting by contributing regularization losses. Our empirical evaluation with Mujoco benchmarks shows that we can successfully learn from very sparse and scarce expert data. Moreover, (i) the quality of the learned policies is often comparable to those learned with full expert trajectories, and (ii) the number of training steps required to learn from sparse data is similar to the number of training steps when the agent has access to full expert trajectories.