Electronic structure problems are key to many insights in a wide variety of scientific fields, including chemistry, materials science, and drug discovery. Current ab initio methods, such as density functional theory (DFT), for calculating the ground state electronic density of a system and its corresponding energy are computationally expensive. To reduce the computational costs, machine learning techniques have recently been applied to compute the ground state energy and in a few cases, the electronic density as well. In this work we introduce a technique for calculating the ground state electronic density at a reduced computational cost relative to DFT. Our method utilizes tools from optimal transport and uses a machine learning model reminiscent of a conditional adversarial network with a U-net architecture.