While the performance of face alignment models has been improving over the years, they still need large, annotated datasets during their training to perform well. In this paper, we propose a new architecture to perform face alignment with limited training data. Our model is based on StyleGAN, a popular architecture in the image generation domain, and takes advantage of its strong generative power to generate accurate facial landmark heatmaps of real face images, using only a small amount of training data. Even when trained down to only 50 samples, our model can still predict accurate facial landmarks. It exceeds state-of-the-art on several face alignment datasets in the low training data regime.