从无配对数据中学习结构化潜在变量，实现半监督聚类与配对样本生成

Quantifying variability in a target population relative to a reference population is central to many scientific and clinical problems (e.g., diseased vs. healthy). Yet, without paired data and in the presence of heterogeneous target variation, existing methods struggle to separate multiple modes of target-specific variation. We propose \textit{CASL-VAE}, a deep contrastive latent variable model that learns structured latent generative factors from unpaired data. CASL-VAE factorizes variation into continuous common latent factors shared across populations and hierarchical salient latent factors that model target-specific heterogeneity as discrete subtypes and continuous within-subtype variation. Using variational inference, we show how approximate joint likelihood optimization over reference and target domains can be performed using unpaired data, providing a principled basis for paired-sample generation and cross-domain analysis. We validate CASL-VAE on semi-synthetic neuroimaging data, demonstrating improved subtype recovery and paired-sample generation compared to baseline clustering and generative models. We also validate its ability to reveal biologically plausible heterogeneity in Alzheimer's disease.