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Neural oscillations in the form of electroencephalogram (EEG) can reveal underlying brain functions, such as cognition, memory, perception, and consciousness. A comprehensive EEG computational model provides not only a stochastic procedure that directly generates data but also insights to further understand the neurological mechanisms. Here, we propose a generative and inference approach that combines the complementary benefits of probabilistic graphical models and generative adversarial networks (GANs) for EEG signal modeling. We investigate the method’s ability to jointly learn coherent generation and inverse inference models on the CHI-MIT epilepsy multi-channel EEG dataset. We further study the efficacy of the learned representations in epilepsy seizure detection formulated as an unsupervised learning problem. Quantitative and qualitative experimental results demonstrate the effectiveness and efficiency of our approach.