Data Augmentation (DA) is a technique to increase the quantity and diversity of the training data, and by that alleviate overfitting and improve generalisation. However, standard DA produces synthetic data for augmentation with limited diversity. Generative Adversarial Networks (GANs) may unlock additional information in a dataset by generating synthetic samples having the appearance of real images. However, these models struggle to simultaneously address three key requirements: fidelity and high-quality samples; diversity and mode coverage; and fast sampling. Indeed, GANs generate high-quality samples rapidly, but have poor mode coverage, limiting their adoption in DA applications. We propose LatentAugment, a DA strategy that overcomes the low diversity of GANs, opening up for use in DA applications. Without external supervision, LatentAugment modifies latent vectors and moves them into latent space regions to maximise the synthetic images' diversity and fidelity. It is also agnostic to the dataset and the downstream task. A wide set of experiments shows that LatentAugment improves the generalisation of a deep model translating from MRI-to-CT beating both standard DA as well GAN-based sampling. We further demonstrate its effectiveness when translating from low-energy mammograms to dual-energy subtracted images in contrast-enhanced spectral mammography. Moreover, still in comparison with GAN-based sampling, LatentAugment synthetic samples show superior mode coverage and diversity. Code is available at: https://github.com/ltronchin/LatentAugment.