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One-shot generative domain adaption aims to transfer a pre-trained generator on one domain to a new domain using one reference image only. However, it remains very challenging for the adapted generator (i) to generate diverse images inherited from the pre-trained generator while (ii) faithfully acquiring the domain-specific attributes and styles of the reference image. In this paper, we present a novel one-shot generative domain adaption method, i.e., DiFa, for diverse generation and faithful adaptation. For global-level adaptation, we leverage the difference between the CLIP embedding of reference image and the mean embedding of source images to constrain the target generator. For local-level adaptation, we introduce an attentive style loss which aligns each intermediate token of adapted image with its corresponding token of the reference image. To facilitate diverse generation, selective cross-domain consistency is introduced to select and retain the domain-sharing attributes in the editing latent $\mathcal{W}+$ space to inherit the diversity of pre-trained generator. Extensive experiments show that our method outperforms the state-of-the-arts both quantitatively and qualitatively, especially for the cases of large domain gaps. Moreover, our DiFa can easily be extended to zero-shot generative domain adaption with appealing results. Code is available at https://github.com/1170300521/DiFa.