Vision-based path following allows robots to autonomously repeat manually taught paths. Stereo Visual Teach and Repeat (VT\&R) accomplishes accurate and robust long-range path following in unstructured outdoor environments across changing lighting, weather, and seasons by relying on colour-constant imaging and multi-experience localization. We leverage multi-experience VT\&R together with two datasets of outdoor driving on two separate paths spanning different times of day, weather, and seasons to teach a deep neural network to predict relative pose for visual odometry (VO) and for localization with respect to a path. In this paper we run experiments exclusively on datasets to study how the network generalizes across environmental conditions. Based on the results we believe that our system achieves relative pose estimates sufficiently accurate for in-the-loop path following and that it is able to localize radically different conditions against each other directly (i.e. winter to spring and day to night), a capability that our hand-engineered system does not have.