COVID-19 image analysis has mostly focused on diagnostic tasks using single timepoint scans acquired upon disease presentation or admission. We present a deep learning-based approach to predict lung infiltrate progression from serial chest radiographs (CXRs) of COVID-19 patients. Our method first utilizes convolutional neural networks (CNNs) for feature extraction from patches within the concerned lung zone, and also from neighboring and remote boundary regions. The framework further incorporates a multi-scale Gated Recurrent Unit (GRU) with a correlation module for effective predictions. The GRU accepts CNN feature vectors from three different areas as input and generates a fused representation. The correlation module attempts to minimize the correlation loss between hidden representations of concerned and neighboring area feature vectors, while maximizing the loss between the same from concerned and remote regions. Further, we employ an attention module over the output hidden states of each encoder timepoint to generate a context vector. This vector is used as an input to a decoder module to predict patch severity grades at a future timepoint. Finally, we ensemble the patch classification scores to calculate patient-wise grades. Specifically, our framework predicts zone-wise disease severity for a patient on a given day by learning representations from the previous temporal CXRs. Our novel multi-institutional dataset comprises sequential CXR scans from N=93 patients. Our approach outperforms transfer learning and radiomic feature-based baseline approaches on this dataset.