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In this paper, we propose a Bidirectional Attention Network (BANet), an end-to-end framework for monocular depth estimation (MDE) that addresses the limitation of effectively integrating local and global information in convolutional neural networks. The structure of this mechanism derives from a strong conceptual foundation of neural machine translation, and presents a light-weight mechanism for adaptive control of computation similar to the dynamic nature of recurrent neural networks. We introduce bidirectional attention modules that utilize the feed-forward feature maps and incorporate the global context to filter out ambiguity. Extensive experiments reveal the high degree of capability of this bidirectional attention model over feed-forward baselines and other state-of-the-art methods for monocular depth estimation on two challenging datasets -- KITTI and DIODE. We show that our proposed approach either outperforms or performs at least on a par with the state-of-the-art monocular depth estimation methods with less memory and computational complexity.