Efficient skill acquisition is crucial for creating versatile robots. One intuitive way to teach a robot new tricks is to enable it to match its behavior to a teacher’s demonstration of the task at hand. This approach is known as imitation learning. Classical methods of imitation learning suffer from the correspondence problem, i.e., when the actions of the teacher are not directly observed or the anatomy of the teacher and the robot differ substantially. To address the correspondence problem, we propose to learn a robot-specific controller that directly matches robot trajectories with demonstrated ones. We use long-term predictions from a learned probabilistic model of the robot’s forward dynamics to match the predicted trajectory distribution with the distribution over observed expert trajectories by minimizing the Kullback-Leibler divergence between these trajectory distributions. The power of the resulting approach is demonstrated by imitating human behavior with a tendon-driven, compliant robotic arm with complex dynamics.