VarMatch: Variational Consistency and Test-Time Adaptation for Semi-Supervised Domain Generalization

Semi-supervised domain generalization (SSDG) aims to generalize to unseen domains using only a few labeled examples per class and additional unlabeled data from multiple source domains. In this setting, limited supervision makes it difficult to learn reliable class structure, while domain shift can cause the learned structure to become misaligned with target data. We introduce VarMatch, a variational latent-space framework that combines stochastic consistency training with source-aware and frozen test-time adaptation. During training, pseudo-labels obtained from weakly augmented examples supervise two complementary views: an image-space augmentation and a variance-scaled stochastic perturbation of the learned latent representation. This encourages predictions to remain consistent under both input-level and representation-level variations. At test time, VarMatch keeps the encoder and classifier frozen, aligns target representations with source class structure, and estimates target-aware class prototypes from confident target samples while excluding samples that provide little evidence of domain shift. Adaptation operates without network-parameter updates and uses deterministic latent representations. Across PACS, OfficeHome, Digits-DG, and miniDomainNet with 5 and 10 labels per class, VarMatch improves over the strongest semi-supervised domain-generalization baseline by 2.37-6.22 percentage points. Its frozen, source-aware adaptation outperforms evaluated parameter-free alternatives and is competitive with methods that update the encoder.