Title: Do Perceptually Aligned Gradients Imply Robustness?. Abstract: Deep learning-based networks have achieved unprecedented success in numerous tasks, among which image classification. Despite these remarkable achievements, recent studies have demonstrated that such classification networks are easily fooled by small malicious perturbations, also known as adversarial examples. This security weakness led to extensive research aimed at obtaining robust models. Beyond the clear robustness benefits of such models, it was also observed that their gradients with respect to the input align with human perception. Several works have identified Perceptually Aligned Gradients (PAG) as a byproduct of robust training, but none have considered it as a standalone phenomenon nor studied its own implications. In this work, we focus on this trait and test whether \emph{Perceptually Aligned Gradients imply Robustness}. To this end, we develop a novel objective to directly promote PAG in training classifiers and examine whether models with such gradients are more robust to adversarial attacks. We present both heuristic and principled ways for obtaining target PAGs, which our method aims to learn. Specifically, we harness recent findings in score-based generative modeling as a source for PAG. Extensive experiments on CIFAR-10 and STL validate that models trained with our method have improved robust performance, exposing the surprising bidirectional connection between PAG and robustness.