Adversarial Training (AT) and Virtual Adversarial Training (VAT) are the regularization techniques that train Deep Neural Networks (DNNs) with adversarial examples generated by adding small but worst-case perturbations to input examples. In this paper, we propose xAT and xVAT, new adversarial training algorithms that generate multiplicative perturbations to input examples for robust training of DNNs. Such perturbations are much more perceptible and interpretable than their additive counterparts exploited by AT and VAT. Furthermore, the multiplicative perturbations can be generated transductively or inductively, while the standard AT and VAT only support a transductive implementation. We conduct a series of experiments that analyze the behavior of the multiplicative perturbations and demonstrate that xAT and xVAT match or outperform state-of-the-art classification accuracies across multiple established benchmarks while being about 30% faster than their additive counterparts. Our source code can be found at https://github.com/sndnyang/xvat