Adapting large-scale foundation models to new domains with limited supervision remains a fundamental challenge due to latent distribution mismatch, unstable optimization dynamics, and miscalibrated uncertainty propagation. This paper introduces an uncertainty-aware probabilistic latent transport framework that formulates domain adaptation as a stochastic geometric alignment problem in representation space. A Bayesian transport operator is proposed to redistribute latent probability mass along Wasserstein-type geodesic trajectories, while a PAC-Bayesian regularization mechanism constrains posterior model complexity to mitigate catastrophic overfitting. The proposed formulation yields theoretical guarantees on convergence stability, loss landscape smoothness, and sample efficiency under distributional shift. Empirical analyses demonstrate substantial reduction in latent manifold discrepancy, accelerated transport energy decay, and improved covariance calibration compared with deterministic fine-tuning and adversarial domain adaptation baselines. Furthermore, bounded posterior uncertainty evolution indicates enhanced probabilistic reliability during cross-domain transfer. By establishing a principled connection between stochastic optimal transport geometry and statistical generalization theory, the proposed framework provides new insights into robust adaptation of modern foundation architectures operating in heterogeneous environments. These findings suggest that uncertainty-aware probabilistic alignment constitutes a promising paradigm for reliable transfer learning in next-generation deep representation systems.

翻译：将大规模基础模型适应到标注样本有限的新领域是一个根本性挑战，其根源在于潜在分布不匹配、优化动态不稳定以及不确定性传播校准不当。本文提出了一种不确定性感知的概率潜在传输框架，将域自适应形式化为表示空间中的随机几何对齐问题。该框架引入贝叶斯传输算子，沿着Wasserstein型测地线轨迹重新分布潜在概率质量，同时采用PAC-贝叶斯正则化机制约束后验模型复杂度以缓解灾难性过拟合。所提公式在分布偏移条件下给出了收敛稳定性、损失景观平滑性和样本效率的理论保证。实证分析表明，与确定性微调和对抗性域自适应基线相比，该方法显著降低了潜在流形差异，加速了传输能量衰减，并改善了协方差校准。此外，有界后验不确定性演化表明跨域迁移期间的概率可靠性得到增强。通过在随机最优输运几何与统计泛化理论之间建立原理性联系，所提框架为异构环境中现代基础架构的鲁棒自适应提供了新见解。这些发现表明，不确定性感知的概率对齐构成了下一代深度表示系统中可靠迁移学习的一个有前景的范式。