In this paper, we propose a unified information theoretic framework for learning-motivated methods aimed at odometry estimation, a crucial component of many robotics and vision tasks such as navigation and virtual reality where relative camera poses are required in real time. We formulate this problem as optimizing a variational information bottleneck objective function, which eliminates pose-irrelevant information from the latent representation. The proposed framework provides an elegant tool for performance evaluation and understanding in information-theoretic language. Specifically, we bound the generalization errors of the deep information bottleneck framework and the predictability of the latent representation. These provide not only a performance guarantee but also practical guidance for model design, sample collection, and sensor selection. Furthermore, the stochastic latent representation provides a natural uncertainty measure without the needs for extra structures or computations. Experiments on two well-known odometry datasets demonstrate the effectiveness of our method.