- Abstract: The work investigates deep generative models, which allow us to use training data from one domain to build a model for another domain. We propose the Variational Bi-domain Triplet Autoencoder (VBTA) that learns a joint distribution of objects from different domains. We extend the VBTAs objective function by the relative constraints or triplets that sampled from the shared latent space across domains. In other words, we combine the deep generative models with a metric learning ideas in order to improve the final objective with the triplets information. The performance of the VBTA model is demonstrated on different tasks: image-to-image translation, bi-directional image generation and cross-lingual document classification.