In this work, we consider the use of a model-based decoder in combination with an unsupervised learning strategy for direction-of-arrival (DoA) estimation. Relying only on unlabeled training data we show in our analysis that we can outperform existing unsupervised machine learning methods and classical methods. The proposed approach consists of introducing a model-based decoder in an autoencoder architecture which leads to a meaningful representation of the statistical model in the latent space of the autoencoder. Our numerical simulations show that the performance of the presented approach is not affected by correlated signals and performs well for both, uncorrelated and correlated, scenarios. This is a result of the fact, that, in the proposed framework, the signal covariance matrix and the DOAs are estimated simultaneously.