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Robot control problems are often structured with a policy function that maps state values into control values, but in many dynamic problems the observed state can have a difficult to characterize relationship with useful policy actions. In this paper we present a new method for learning state embeddings from plans or other forms of demonstrations such that the embedding space has a specified geometric relationship with the demonstrations. We present a novel variational framework for learning these embeddings that attempts to optimize trajectory linearity in the learned embedding space. We show how these embedding spaces can then be used as an augmentation to the robot state in reinforcement learning problems. We use kinodynamic planning to generate training trajectories for some example environments, and then train embedding spaces for these environments. We show empirically that observing a system in the learned embedding space improves the performance of policy gradient reinforcement learning algorithms, particularly by reducing the variance between training runs. Our technique is limited to environments where demonstration data is available, but places no limits on how that data is collected. Our embedding technique provides a way to transfer domain knowledge from existing technologies such as planning and control algorithms, into more flexible policy learning algorithms, by creating an abstract representation of the robot state with meaningful geometry.