Abstract: Domain Generalization (DG) aims to resolve distribution shifts between source and target domains, and current DG methods are default to the setting that data from source and target domains share identical categories. Nevertheless, there exists unseen classes from target domains in practical scenarios. To address this issue, Open Set Domain Generalization (OSDG) has emerged and several methods have been exclusively proposed. However, most existing methods adopt complex architectures with slight improvement compared with DG methods. Recently, vision-language models (VLMs) have been introduced in DG following the fine-tuning paradigm, but consume huge training overhead with large vision models. Therefore, in this paper, we innovate to transfer knowledge from VLMs to lightweight vision models and improve the robustness by introducing Perturbation Distillation (PD) from three perspectives, including Score, Class and Instance (SCI), named SCI-PD. Moreover, previous methods are oriented by the benchmarks with identical and fixed splits, ignoring the divergence between source domains. These methods are revealed to suffer from sharp performance decay with our proposed new benchmark Hybrid Domain Generalization (HDG) and a novel metric $H^{2}$-CV, which construct various splits to comprehensively assess the robustness of algorithms. Extensive experiments demonstrate that our method outperforms state-of-the-art algorithms on multiple datasets, especially improving the robustness when confronting data scarcity.