Matrix factorisation methods decompose multivariate observations as linear combinations of latent feature vectors. The Indian Buffet Process (IBP) provides a way to model the number of latent features required for a good approximation in terms of regularised reconstruction error. Previous work has focussed on latent feature vectors with independent entries. We extend the model to include nondiagonal latent covariance structures representing characteristics such as smoothness. This is done by . Using simulations we demonstrate that under appropriate conditions a smoothness prior helps to recover the true latent features, while denoising more accurately. We demonstrate our method on a real neuroimaging dataset, where computational tractability is a sufficient challenge that the efficient strategy presented here is essential.