  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
