In this paper, we propose a semi-supervised learning (SSL) technique for training deep neural networks (DNNs) to generate speaker-discriminative acoustic embeddings (speaker embeddings). Obtaining large amounts of speaker recognition train-ing data can be difficult for desired target domains, especially under privacy constraints. The proposed technique reduces requirements for labelled data by leveraging unlabelled data. The technique is a variant of virtual adversarial training (VAT) [1] in the form of a loss that is defined as the robustness of the speaker embedding against input perturbations, as measured by the cosine-distance. Thus, we term the technique cosine-distance virtual adversarial training (CD-VAT). In comparison to many existing SSL techniques, the unlabelled data does not have to come from the same set of classes (here speakers) as the labelled data. The effectiveness of CD-VAT is shown on the 2750+ hour VoxCeleb data set, where on a speaker verification task it achieves a reduction in equal error rate (EER) of 11.1% relative to a purely supervised baseline. This is 32.5% of the improvement that would be achieved from supervised training if the speaker labels for the unlabelled data were available.