  Deep neural networks are susceptible to human imperceptible adversarial
perturbations. One of the strongest defense mechanisms is \emph{Adversarial
Training} (AT). In this paper, we aim to address two predominant problems in
AT. First, there is still little consensus on how to set hyperparameters with a
performance guarantee for AT research, and customized settings impede a fair
comparison between different model designs in AT research. Second, the robustly
trained neural networks struggle to generalize well and suffer from tremendous
overfitting. This paper focuses on the primary AT framework - Projected
Gradient Descent Adversarial Training (PGD-AT). We approximate the dynamic of
PGD-AT by a continuous-time Stochastic Differential Equation (SDE), and show
that the diffusion term of this SDE determines the robust generalization. An
immediate implication of this theoretical finding is that robust generalization
is positively correlated with the ratio between learning rate and batch size.
We further propose a novel approach, \emph{Diffusion Enhanced Adversarial
Training} (DEAT), to manipulate the diffusion term to improve robust
generalization with virtually no extra computational burden. We theoretically
show that DEAT obtains a tighter generalization bound than PGD-AT. Our
empirical investigation is extensive and firmly attests that DEAT universally
outperforms PGD-AT by a significant margin.
