We propose a new efficient way to sample from a Variational Autoencoder in the challenging low sample size setting. This method reveals particularly well suited to perform data augmentation in such a low data regime and is validated across various standard and real-life data sets. In particular, this scheme allows to greatly improve classification results on the OASIS database where balanced accuracy jumps from 80.7% for a classifier trained with the raw data to 88.6% when trained only with the synthetic data generated by our method. Such results were also observed on 3 standard data sets and with other classifiers. A code is available at https://github.com/clementchadebec/Data_Augmentation_with_VAE-DALI.