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State-of-the-art face recognition models are computationally expensive for mobile applications. Training lightweight face recognition models also requires large identity-labeled datasets, raising privacy and ethical concerns. Generating synthetic datasets for training is also challenging, and there is a significant gap in performance between models trained on real and synthetic face datasets. We propose a new framework (called SynthDistill) to train lightweight face recognition models by distilling the knowledge from a pretrained teacher model using synthetic data. We generate synthetic face images without identity labels, mitigating the problems in the intra-class variation generation of synthetic datasets, and dynamically sample from the intermediate latent space of a face generator network to generate new variations of the challenging images while further exploring new face images. The results on different benchmarking real face recognition datasets demonstrate the superiority of SynthDistill compared to training on previous synthetic datasets, achieving a verification accuracy of 99.52% on the LFW dataset with a lightweight network. The results also show that SynthDistill significantly narrows the gap between real and synthetic data training. The source code of our experiments is publicly available to facilitate the reproducibility of our work.