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With the development of higher resolution contents and displays, its significant volume poses significant challenges to the goals of acquiring, transmitting, compressing, and displaying high-quality video content. In this paper, we propose a new deep learning video compression architecture that does not require motion estimation, which is the most expensive element of modern hybrid video compression codecs like H.264 and HEVC. Our framework exploits the regularities inherent to video motion, which we capture by using displaced frame differences as video representations to train the neural network. In addition, we propose a new space-time reconstruction network based on both an LSTM model and a UNet model, which we call LSTM-UNet. The new video compression framework has three components: a Displacement Calculation Unit (DCU), a Displacement Compression Network (DCN), and a Frame Reconstruction Network (FRN). The DCU removes the need for motion estimation found in hybrid codecs and is less expensive. In the DCN, an RNN-based network is utilized to compress displaced frame differences as well as retain temporal information between frames. The LSTM-UNet is used in the FRN to learn space-time differential representations of videos. Our experimental results show that our compression model, which we call the MOtionless VIdeo Codec (MOVI-Codec), learns how to efficiently compress videos without computing motion. Our experiments show that MOVI-Codec outperforms the Low-Delay P veryfast setting of the video coding standard H.264 and exceeds the performance of the modern global standard HEVC codec, using the same setting, as measured by MS-SSIM, especially on higher resolution videos. In addition, our network outperforms the latest H.266 (VVC) codec at higher bitrates, when assessed using MS-SSIM, on high-resolution videos.