Plasma tomography consists of reconstructing a two-dimensional radiation profile of a poloidal cross section of a fusion device based on line-integrated measurements along several lines of sight. The reconstruction process is computationally intensive, and in practice, only a few reconstructions are usually computed per pulse. In this work, we trained a deep neural network based on a large collection of sample tomograms that have been produced at JET over several years. Once trained, the network is able to reproduce those results with high accuracy. More importantly, it can compute all the tomographic reconstructions for a given pulse in just a few seconds. This makes it possible to visualize several phenomena-such as plasma heating, disruptions, and impurity transport-over the course of the entire pulse.