This paper applies inter-session variability modelling and joint factor analysis to face authentication using Gaussian mixture models. These techniques, originally developed for speaker authentication, aim to explicitly model and remove detrimental within-client (inter-session) variation from client models. We apply the techniques to face authentication on the publicly-available BANCA, SCface and MOBIO databases. We propose a face authentication protocol for the challenging SCface database, and provide the first results on the MOBIO still face protocol. The techniques provide relative reductions in error rate of up to 44%, using only limited training data. On the BANCA database, our results represent a 31% reduction in error rate when benchmarked against previous work.