This paper presents a theoretical analysis on using unlabeled data (under a self-training scheme of a Gaussian model) to improve the robustness against adversarial noise, followed by a semi-supervised learning method to learn deep networks. The empirical results are state-of-the-art. However, this paper heavily overlaps with another paper "Are Labels Required for Improving Adversarial Robustness?". As a condition to accepting and including the paper in the proceedings, put the following disclaimer in the footnote on the first page: "The authors declare that the present paper is independent of "Are Labels Required for Improving Adversarial Robustness?"."