Network quantization is an essential procedure in deep learning for development of efficient fixed-point inference models on mobile or edge platforms. However, as datasets grow larger and privacy regulations become stricter, data sharing for model compression gets more difficult and restricted. In this paper, we consider data-free network quantization with synthetic data. The synthetic data are generated from a generator, while no data are used in training the generator and in quantization. To this end, we propose data-free adversarial knowledge distillation, which minimizes the maximum distance between the outputs of the teacher and the (quantized) student for any adversarial samples from a generator. To generate adversarial samples similar to the original data, we additionally propose matching statistics from the batch normalization layers for generated data and the original data in the teacher. Furthermore, we show the gain of producing diverse adversarial samples by using multiple generators and multiple students. Our experiments show the state-of-the-art data-free model compression and quantization results for (wide) residual networks and MobileNet on SVHN, CIFAR-10, CIFAR-100, and Tiny-ImageNet datasets. The accuracy losses compared to using the original datasets are shown to be very minimal.