Title: Variational Deterministic Uncertainty Quantification. Abstract: Building on recent advances in uncertainty quantification using a single deep deterministic model (DUQ), we introduce variational Deterministic Uncertainty Quantification (vDUQ). We overcome several shortcomings of DUQ by recasting it as a Gaussian process (GP) approximation. Our principled approximation is based on an inducing point GP in combination with Deep Kernel Learning. This enables vDUQ to use rigorous probabilistic foundations, and work not only on classification but also on regression problems. We avoid uncertainty collapse away from the training data by regularizing the spectral norm of the deep feature extractor. Our method matches SotA accuracy, 96.2\% on CIFAR-10, while maintaining the speed of softmax models, and provides uncertainty estimates competitive with Deep Ensembles. We demonstrate our method in regression problems and by estimating uncertainty in causal inference for personalized medicine