AbstractWe address the problem of enhancing model robustness through regularization. Specifically, we focus on methods that regularize the model posterior difference between clean and noisy inputs. Theoretically, we provide a connection of two recent methods, Jacobian Regularization and Virtual Adversarial Training, under this framework. Additionally, we generalize the posterior differential regularization to the family of f-divergences and characterize the overall framework in terms of the Jacobian matrix. Empirically, we compare those regularizations and standard BERT training on a diverse set of tasks to provide a comprehensive profile of their effect on model generalization. For both fully supervised and semi-supervised settings, we show that regularizing the posterior difference with f-divergence can result in well-improved model robustness. In particular, with a proper f-divergence, a BERT-base model can achieve comparable generalization as its BERT-large counterpart for in-domain, adversarial and domain shift scenarios, indicating the great potential of the proposed framework for enhancing NLP model robustness.