As Deep Learning continues to yield successful applications in Computer
Vision, the ability to quantify all forms of uncertainty is a paramount
requirement for its safe and reliable deployment in the real-world. In this
work, we leverage the formulation of variational inference in function space,
where we associate Gaussian Processes (GPs) to both Bayesian CNN priors and
variational family. Since GPs are fully determined by their mean and covariance
functions, we are able to obtain predictive uncertainty estimates at the cost
of a single forward pass through any chosen CNN architecture and for any
supervised learning task. By leveraging the structure of the induced covariance
matrices, we propose numerically efficient algorithms which enable fast
training in the context of high-dimensional tasks such as depth estimation and
semantic segmentation. Additionally, we provide sufficient conditions for
constructing regression loss functions whose probabilistic counterparts are
compatible with aleatoric uncertainty quantification.