The study of cross-domain mapping without supervision has recently attracted much attention. Much of the recent progress was enabled by the use of adversarial training as well as cycle constraints. The practical difficulty of adversarial training motivates research into non-adversarial methods. In a recent paper, it was shown that cross-domain mapping is possible without the use of cycles or GANs. Although promising, this approach suffers from several drawbacks including costly inference and an optimization variable for every training example preventing the method from using large training sets. We present an alternative approach which is able to achieve non-adversarial mapping using a novel form of Variational Auto-Encoder. Our method is much faster at inference time, is able to leverage large datasets and has a simple interpretation.