- Abstract: Quantifying, enforcing and implementing fairness emerged as a major topic in machine learning. We investigate these questions in the context of deep learning. Our main algorithmic and theoretical tool is the computational estimation of similarities between probability, ``\`a la Wasserstein'', using adversarial networks. This idea is flexible enough to investigate different fairness constrained learning tasks, which we model by specifying properties of the underlying data generative process. The first setting considers bias in the generative model which should be filtered out. The second model is related to the presence of nuisance variables in the observations producing an unwanted bias for the learning task. For both models, we devise a learning algorithm based on approximation of Wasserstein distances using adversarial networks. We provide formal arguments describing the fairness enforcing properties of these algorithm in relation with the underlying fairness generative processes. Finally we perform experiments, both on synthetic and real world data, to demonstrate empirically the superiority of our approach compared to state of the art fairness algorithms as well as concurrent GAN type adversarial architectures based on Jensen divergence.