We propose a structured variational inference model for disentangling observable evidence of disease (e.g. brain lesions or atrophy) from subject-specific anatomy in brain MRIs. With flexible, partially autoregressive priors, our model (1) addresses the subtle and detailed dependencies that typically exist between anatomical and pathological generating factors of an MRI to ensure the validity of generated samples; (2) preserves and disentangles finer pathological details pertaining to one’s disease state. We additionally demonstrate, by providing supervision to a subset of latent units, that (1) a partially supervised latent space achieves a higher degree of disentanglement between evidence of disease and subject-specific anatomy; (2) when the prior is formulated with an autoregressive structure, knowledge from the supervision can propagate to the unsupervised latent units, resulting in more informative latent representations capable of modelling anatomy-pathology interdependencies.