  Unsupervised Multiple Domain Translation is the task of transforming data
from one domain to other domains without having paired data to train the
systems. Typically, methods based on Generative Adversarial Networks (GANs) are
used to address this task. However, our proposal exclusively relies on a
modified version of a Variational Autoencoder. This modification consists of
the use of two latent variables disentangled in a controlled way by design. One
of this latent variables is imposed to depend exclusively on the domain, while
the other one must depend on the rest of the variability factors of the data.
Additionally, the conditions imposed over the domain latent variable allow for
better control and understanding of the latent space. We empirically
demonstrate that our approach works on different vision datasets improving the
performance of other well known methods. Finally, we prove that, indeed, one of
the latent variables stores all the information related to the domain and the
other one hardly contains any domain information.
