Causal mapping of the functional organisation of the human brain requires evidence of \textit{necessity} available at adequate scale only from pathological lesions of natural origin. This demands inferential models with sufficient flexibility to capture both the observable distribution of pathological damage and the unobserved distribution of the neural substrate. Current model frameworks -- both mass-univariate and multivariate -- either ignore distributed lesion-deficit relations or do not model them explicitly, relying on featurization incidental to a predictive task. Here we initiate the application of deep generative neural network architectures to the task of lesion-deficit inference, formulating it as the estimation of an expressive hierarchical model of the joint lesion and deficit distributions conditioned on a latent neural substrate. We implement such deep lesion deficit inference with variational convolutional volumetric auto-encoders. We introduce a comprehensive framework for lesion-deficit model comparison, incorporating diverse candidate substrates, forms of substrate interactions, sample sizes, noise corruption, and population heterogeneity. Drawing on 5500 volume images of ischaemic stroke, we show that our model outperforms established methods by a substantial margin across all simulation scenarios, including comparatively small-scale and noisy data regimes. Our analysis justifies the widespread adoption of this approach, for which we provide an open source implementation: https://github.com/guilherme-pombo/vae_lesion_deficit