Domain Adaptive Object Detection (DAOD) transfers knowledge from a labeled source domain to an unannotated target domain under closed-set assumption. Universal DAOD (UniDAOD) extends DAOD to handle open-set, partial-set, and closed-set domain adaptation. In this paper, we first unveil two issues: domain-private category alignment is crucial for global-level features, and the domain probability heterogeneity of features across different levels. To address these issues, we propose a novel Dual Probabilistic Alignment (DPA) framework to model domain probability as Gaussian distribution, enabling the heterogeneity domain distribution sampling and measurement. The DPA consists of three tailored modules: the Global-level Domain Private Alignment (GDPA), the Instance-level Domain Shared Alignment (IDSA), and the Private Class Constraint (PCC). GDPA utilizes the global-level sampling to mine domain-private category samples and calculate alignment weight through a cumulative distribution function to address the global-level private category alignment. IDSA utilizes instance-level sampling to mine domain-shared category samples and calculates alignment weight through Gaussian distribution to conduct the domain-shared category domain alignment to address the feature heterogeneity. The PCC aggregates domain-private category centroids between feature and probability spaces to mitigate negative transfer. Extensive experiments demonstrate that our DPA outperforms state-of-the-art UniDAOD and DAOD methods across various datasets and scenarios, including open, partial, and closed sets. Codes are available at \url{https://github.com/zyfone/DPA}.
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