Rapidly generating accurate extremes from an observational dataset is crucial when seeking to estimate risks associated with the occurrence of future extremes which could be larger than those already observed. Many applications ranging from the occurrence of natural disasters to financial crashes are involved. This paper details a variational auto-encoder (VAE) approach for sampling multivariate extremes. The proposed architecture is based on the extreme value theory (EVT) and more particularly on the notion of multivariate functions with regular variations. Experiments conducted on synthetic datasets as well as on a dataset of discharge measurements along Danube river network illustrate the relevance of our approach.