Space-time visualizations of macroscopic or microscopic traffic variables is a qualitative tool used by traffic engineers to understand and analyze different aspects of road traffic dynamics. We present a deep learning method to learn the macroscopic traffic speed dynamics from these space-time visualizations, and demonstrate its application in the framework of traffic state estimation. Compared to existing estimation approaches, our approach allows a finer estimation resolution, eliminates the dependence on the initial conditions, and is agnostic to external factors such as traffic demand, road inhomogeneities and driving behaviors. Our model respects causality in traffic dynamics, which improves the robustness of estimation. We present the high-resolution traffic speed fields estimated for several freeway sections using the data obtained from the Next Generation Simulation Program (NGSIM) and German Highway (HighD) datasets. We further demonstrate the quality and utility of the estimation by inferring vehicle trajectories from the estimated speed fields, and discuss the benefits of deep neural network models in approximating the traffic dynamics.