Robust recommendation aims at capturing true preference of users from noisy data, for which there are two lines of methods have been proposed. One is based on noise injection, and the other is to adopt the generative model Variational Auto-encoder (VAE). However, the existing works still face two challenges. First, the noise injection based methods often draw the noise from a fixed noise distribution given in advance, while in real world, the noise distributions of different users and items may differ from each other due to personal behaviors and item usage patterns. Second, the VAE based models are not expressive enough to capture the true preference since VAE often yields an embedding space of a single modal, while in real world, user-item interactions usually exhibit multi-modality on user preference distribution. In this paper, we propose a novel model called Dual Adversarial Variational Embedding (DAVE) for robust recommendation, which can provide personalized noise reduction for different users and items, and capture the multi-modality of the embedding space, by combining the advantages of VAE and adversarial training between the introduced auxiliary discriminators and the variational inference networks. The extensive experiments conducted on real datasets verify the effectiveness of DAVE on robust recommendation.