The supervised-learning-based morphing attack detection (MAD) solutions achieve outstanding success in dealing with attacks from known morphing techniques and known data sources. However, given variations in the morphing attacks, the performance of supervised MAD solutions drops significantly due to the insufficient diversity and quantity of the existing MAD datasets. To address this concern, we propose a completely unsupervised MAD solution via self-paced anomaly detection (SPL-MAD) by leveraging the existing large-scale face recognition (FR) datasets and the unsupervised nature of convolutional autoencoders. Using general FR datasets that might contain unintentionally and unlabeled manipulated samples to train an autoencoder can lead to a diverse reconstruction behavior of attack and bona fide samples. We analyze this behavior empirically to provide a solid theoretical ground for designing our unsupervised MAD solution. This also results in proposing to integrate our adapted modified self-paced learning paradigm to enhance the reconstruction error separability between the bona fide and attack samples in a completely unsupervised manner. Our experimental results on a diverse set of MAD evaluation datasets show that the proposed unsupervised SPL-MAD solution outperforms the overall performance of a wide range of supervised MAD solutions and provides higher generalizability on unknown attacks. Training codes and pre-trained models are publicly released ^{1 1} https://github.com/meilfang/SPL-MAD.