Abstract: Stereo matching is a core task for many computer vision and robotics applications. Despite their dominance in traditional stereo methods, the hand-crafted Markov Random Field (MRF) models lack sufficient modeling accuracy compared to end-to-end deep models. While deep learning representations have greatly improved the unary terms of the MRF models, the overall accuracy is still severely limited by the hand-crafted pairwise terms and message passing. To address these issues, we propose a neural MRF model, where both potential functions and message passing are designed using data-driven neural networks. Our fully data-driven model is built on the foundation of variational inference theory, to prevent convergence issues and retain stereo MRF's graph inductive bias. To make the inference tractable and scale well to high-resolution images, we also propose a Disparity Proposal Network (DPN) to adaptively prune the search space of disparity. The proposed approach ranks $1^{st}$ on both KITTI 2012 and 2015 leaderboards among all published methods while running faster than 100 ms. This approach significantly outperforms prior global methods, e.g., lowering D1 metric by more than 50% on KITTI 2015. In addition, our method exhibits strong cross-domain generalization and can recover sharp edges. The codes at https://github.com/aeolusguan/NMRF.