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Probabilistic modelling has been an essential tool in medical image analysis, especially for analyzing brain Magnetic Resonance Images (MRI). Recent deep learning techniques for estimating high-dimensional distributions, in particular Variational Autoencoders (VAEs), opened up new avenues for probabilistic modeling. Modelling of volumetric data has remained a challenge, however, because constraints on available computation and training data make it difficult effectively leverage VAEs, which are well-developed for 2D images. We propose a method to model 3D MR brain volumes distribution by combining a 2D slice VAE with a Gaussian model that captures the relationships between slices. We do so by estimating the sample mean and covariance in the latent space of the 2D model over the slice direction. This combined model lets us sample new coherent stacks of latent variables to decode into slices of a volume. We also introduce a novel evaluation method for generated volumes that quantifies how well their segmentations match those of true brain anatomy. We demonstrate that our proposed model is competitive in generating high quality volumes at high resolutions according to both traditional metrics and our proposed evaluation.