Reconstructing high-resolution (HR) information from a low-resolution (LR) data has been of great interest. While most of the so-called super-resolution (SR) models rely on a supervised training with high-resolution ground truth data, in many real-life problems, such ground truth data is either difficult to create or nonexistent. Here, we present a deep learning model for a space-time SR from a sequence of LR images for advection-diffusion problems without the ground truth HR data. We use a state-space representation to reconstruct the HR fields with the mass conservation constraints. The proposed method is verified by using two-dimensional CFD simulations.