Recommendation models based on deep learning are fragile when facing adversarial examples (AE). Adversarial training (AT) is the existing mainstream method to promote the adversarial robustness of recommendation models. However, these AT methods often have two drawbacks. First, they may be ineffective due to the ubiquitous sparsity of interaction data. Second, point-wise perturbation used by these AT methods leads to suboptimal adversarial robustness, because not all examples are equally susceptible to such perturbations. To overcome these issues, we propose a novel method called Cross-domain Distributional Adversarial Training (CDAT) which utilizes a richer auxiliary domain to improve the adversarial robustness of a sparse target domain. CDAT comprises a Domain adversarial network (Dan) and a Cross-domain adversarial example generative network (Cdan). Dan learns a domain-invariant preference distribution which is obtained by aligning user embeddings from two domains and paves the way to leverage the knowledge from another domain for the target domain. Then, by adversarially perturbing the domain-invariant preference distribution under the guidance of a discriminator, Cdan captures an aggressive and imperceptible AE distribution. In this way, CDAT can transfer distributional adversarial robustness from the auxiliary domain to the target domain. The extensive experiments conducted on real datasets demonstrate the remarkable superiority of the proposed CDAT in improving the adversarial robustness of the sparse domain.