Patients with neuropsychiatric disorders, in particular schizophrenia, show a variety of eye movement abnormalities that putatively reflect alterations of perceptual inference, learning and cognitive control. While these abnormalities are consistently found at the group level, a particularly difficult and important challenge is to translate these findings into clinically useful tests for single patients. In this paper, we argue that generative models of eye movement data, which allow for inferring individual computational and physiological mechanisms, could contribute to filling this gap. We present a selective overview of eye movement paradigms with clinical relevance for schizophrenia and review existing computational approaches that rest on (or could be turned into) generative models. We conclude by outlining desirable clinical applications at the individual subject level and discuss the necessary validation studies.