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Wireless links using massive MIMO transceivers are vital for next generation wireless communications networks. Precoding in Massive MIMO transmission requires accurate downlink channel state information (CSI). Many recent works have effectively applied deep learning (DL) to jointly train UE-side compression networks for delay domain CSI and a BS-side decoding scheme. Vitally, these works assume that the full delay domain CSI is available at the UE, but in reality, the UE must estimate the delay domain based on a limited number of frequency domain pilots. In this work, we propose a linear pilot-to-delay estimator (P2DE) that acquires the truncated delay CSI via sparse frequency pilots. We show the accuracy of the P2DE under frequency downsampling, and we demonstrate the P2DE’s efficacy when utilized with existing CSI estimation networks. Additionally, we propose to use trainable compressed sensing (CS) networks in a differential encoding network for time-varying CSI estimation, and we propose a new network, MarkovNet-ISTA-ENet (MN-IE), which combines a CS network for initial CSI estimation and multiple autoencoders to estimate the error terms. We demonstrate that MN-IE has better asymptotic performance than networks comprised of only one type of network.