Unsupervised domain adaptation (UDA) has been widely concerned in the fields of machine learning, pattern recognition, and computer vision. Traditional UDA learning usually assumes that the label spaces of the source and target domains are exactly the same and only needs to solve the problem of sample distribution drift existing between two domains. However, in real world applications, the label spaces between two domains may be different. In this case, there are both sample distribution drift and class spatial difference between domains, namely Universal Domain Adaptation (UniDA) learning scenario. At present, existing works rarely offer theoretical analysis for universal domain adaptation. In this paper, we provide an upper bound of the generalization error for universal domain adaptation. According to the proposed generalization error bound, we propose a novel UniDA algorithm called Joint Distribution Alignment for Universal Domain Adaptation (JAUA), which aligns the joint distributions by minimizing the distribution discrepancy calculated by Chi-Square divergence. Furthermore, we propose a progressive pseudo-labeling method to assign the pseudo labels to unlabeled target samples. The experiment results on six public image datasets demonstrate the superiority of JAUA in handling the UniDA problem.
Dataset condensation aims to construct compact datasets from real data via synthesis or selection. However, existing approaches are ill-suited for diffusion model training: synthetic data generation often yields low-fidelity samples unsuitable for authentic modeling, while real subset selection typically fails to preserve the distributional geometry required by diffusion likelihood objectives. To address this, we propose to reformulate real subset selection as a geometry-aware distribution alignment problem. By incorporating one-sided partial optimal transport, our method selectively aligns a compact subset with the full data distribution while allowing unmatched mass in low-density regions, ensuring the preserved geometric structure necessary for effective diffusion model training. To further ensure distributional fidelity, we complement geometric alignment with lightweight feature-statistics and semantic consistency regularization. An efficient two-stage discrete optimization strategy is proposed to achieve this alignment objective. Extensive experiments across diffusion variants, subset sizes, image resolutions, and training rounds show that our method achieves superior fidelity and distributional coverage in diffusion model training. Codes are available at https://github.com/2018cx/GADC.