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Neuroimaging techniques produce high-dimensional, stochastic data from which it might be challenging to extract high-level knowledge about the phenomena of interest. We address this challenge by applying the generative modelling framework to 1) classify multiple pathologies and 2) recover the neurological mechanisms of those pathologies in a data-driven manner. Our framework learns generative factors of data related to pathologies. We provide an algorithm to decode those factors further and observe how different pathologies affect observed data. We illustrate the applicability of the proposed approach to identifying schizophrenia, either followed or not by auditory verbal hallucinations. We further demonstrate the ability of the framework to learn disease-related mechanisms consistent with current domain knowledge. We also compare the proposed framework with several benchmark approaches and indicate its classification performance and interpretability advantages.