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The requirements of much larger file sizes, different storage formats, and immersive viewing conditions of VR pose significant challenges to the goals of acquiring, transmitting, compressing, and displaying high-quality VR content. At the same time, the great potential of deep learning to advance progress on the video compression problem has driven a significant research effort. Because of the high bandwidth requirements of VR, there has also been significant interest in the use of space-variant, foveated compression protocols. We have integrated these techniques to create an end-to-end deep learning video compression framework. A feature of our new compression model is that it dispenses with the need for expensive search-based motion prediction computations. This is accomplished by exploiting statistical regularities inherent in video motion expressed by displaced frame differences. Foveation protocols are desirable since only a small portion of a video viewed in VR may be visible as a user gazes in any given direction. Moreover, even within a current field of view (FOV), the resolution of retinal neurons rapidly decreases with distance (eccentricity) from the projected point of gaze. In our learning based approach, we implement foveation by introducing a Foveation Generator Unit (FGU) that generates foveation masks which direct the allocation of bits, significantly increasing compression efficiency while making it possible to retain an impression of little to no additional visual loss given an appropriate viewing geometry. Our experiment results reveal that our new compression model, which we call the Foveated MOtionless VIdeo Codec (Foveated MOVI-Codec), is able to efficiently compress videos without computing motion, while outperforming foveated version of both H.264 and H.265 on the widely used UVG dataset and on the HEVC Standard Class B Test Sequences.