Face image synthesis has advanced rapidly in recent years. However, similar success has not been witnessed in related areas such as face single image super-resolution (SISR). The performance of SISR on real-world low-quality face images remains unsatisfactory. In this paper, we demonstrate how to advance the state-of-the-art in face SISR by leveraging style-based generator in unsupervised settings. For real-world low-resolution (LR) face images, we propose a novel unsupervised learning approach by combining style-based generator with relativistic discriminator. With a carefully designed training strategy, we demonstrate our converges faster and better suppresses artifacts than Bulat’s approach. When trained on an ensemble of high-quality datasets (CelebA, AFLW, LS3D-W, and VGGFace2), we report significant visual quality improvements over other competing methods especially for real-world low-quality face images such as those in Widerface. Additionally, we have verified that both our unsupervised approaches are capable of improving the matching performance of widely used face recognition systems such as OpenFace.