Estimating the correspondences between pixels in sequences of images is a critical first step for a myriad of tasks including vision-aided navigation (e.g., visual odometry (VO), visual-inertial odometry (VIO), and visual simultaneous localization and mapping (VSLAM)) and anomaly detection. We introduce a new unsupervised deep neural network architecture called the Visual Inertial Flow (VIFlow) network and demonstrate image correspondence and optical flow estimation by an unsupervised multi-hypothesis deep neural network receiving grayscale imagery and extra-visual inertial measurements. VIFlow learns to combine heterogeneous sensor streams and sample from an unknown, un-parametrized noise distribution to generate several (4 or 8 in this work) probable hypotheses on the pixel-level correspondence mappings between a source image and a target image . We quantitatively benchmark VIFlow against several leading vision-only dense correspondence and flow methods and show a substantial decrease in runtime and increase in efficiency compared to all methods with similar performance to state-of-the-art (SOA) dense correspondence matching approaches. We also present qualitative results showing how VIFlow can be used for detecting anomalous independent motion.