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Traffic matrices (TMs) contain information that is essential for network management, traffic engineering, and anomaly detection. However, constructing a TM through direct traffic measurements has a high administrative and computational cost. A more feasible approach is to estimate the TM from the easily obtainable link load measurements. In this paper, we address the issue of traffic matrix estimation (TME) from link loads using a deep generative model – namely, a variational autoencoder (VAE) – to solve the respective ill-posed inverse problem. In particular, we train the VAE with historical data (previously observed TMs) and we leverage the trained decoder to transform TME into a minimization problem in the latent space, which in turn can be solved by employing a gradient-based optimizer. Furthermore, the trained decoder can be used for traffic matrix synthesis, i.e., for generating synthetic TM examples that …