Abstract The effectiveness of GANs in producing images according to a specific visual domain has shown potential in unsupervised domain adaptation. Source labeled images have been modified to mimic target samples for training classifiers in the target domain, and inverse mappings from the target to the source domain have also been evaluated, without new image generation. In this paper we aim at getting the best of both worlds by introducing a symmetric mapping among domains. We jointly optimize bi-directional image transformations combining them with target self-labeling. We define a new class consistency loss that aligns the generators in the two directions, imposing to preserve the class identity of an image passing through both domain mappings. A detailed analysis of the reconstructed images, a thorough ablation study and extensive experiments on six different settings confirm the power of our approach