Active Domain Adaptation (ADA) has emerged as an attractive technique for assisting domain adaptation by actively annotating a small subset of target samples. Most ADA methods focus on measuring the target representativeness beyond traditional active learning criteria to handle the domain shift problem, while leaving the uncertainty estimation to be performed by an uncalibrated deterministic model. In this work, we introduce a probabilistic framework that captures both data-level and prediction-level uncertainties beyond a point estimate. Specifically, we use variational inference to approximate the joint posterior distribution of latent representation and model prediction. The variational objective of labeled data can be formulated by a variational autoencoder and a latent diffusion classifier, and the objective of unlabeled data can be implemented in a knowledge distillation framework. We utilize adversarial learning to ensure an invariant latent space. The resulting diffusion classifier enables efficient sampling of all possible predictions for each individual to recover the predictive distribution. We then leverage a t-test-based criterion upon the sampling and select informative unlabeled target samples based on the p-value, which encodes both prediction variability and cross-category ambiguity. Experiments on both ADA and Source-Free ADA settings show that our method provides more calibrated predictions than previous ADA methods and achieves favorable performance on three domain adaptation datasets.