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Understanding how neural structure varies across individuals is critical for characterizing the effects of disease, learning, and aging on the brain. However, disentangling the different factors that give rise to individual variability is still an outstanding challenge. In this paper, we introduce a deep generative modeling approach to find different modes of variation across many individuals. Our approach starts with training a variational autoencoder on a collection of auto-fluorescence images from a little over 1,700 mouse brains at 25 μ m resolution. We then tap into the learned factors and validate the model’s expressiveness, via a novel bi-directional technique that makes structured perturbations to both, the high-dimensional inputs of the network, as well as the low-dimensional latent variables in its bottleneck. Our results demonstrate that through coupling generative modeling frameworks with structured perturbations, it is possible to probe the latent space of the generative model to provide insights into the representations of brain structure formed in deep networks.