CD-SSDG: Cross-Domain SSL & Generalization

• CD-SSDG is a learning paradigm that integrates limited labeled data with abundant unlabeled samples from multiple domains to achieve unseen target generalization.
• It employs SSL backbones enhanced by domain-aware pseudo-labeling, feature alignment, and cross-domain regularization to overcome distribution shifts.
• Empirical studies show that CD-SSDG methods significantly outperform traditional DG and SSL baselines, especially in low-label regimes across varied benchmarks.

Cross-Domain Semi-Supervised Domain Generalization (CD-SSDG) is a learning setting at the intersection of domain generalization (DG) and semi-supervised learning (SSL), in which training uses limited labeled data together with larger unlabeled data drawn from multiple domains, while testing is performed on an unseen target domain under distribution shift. Across the literature, the term is used in two closely related ways. In the standard SSDG formulation, each source domain contains a small labeled subset and a larger unlabeled subset, and the model must generalize to an unseen target domain (Qi et al., 2022). In a stricter formulation, often called CD-SSDG, labeled and unlabeled training data themselves come from different source distributions—for example, one labeled source domain and multiple unlabeled source domains—so domain shifts exist both within training and between training and test domains (Song et al., 25 Sep 2025). Early work such as DGSML established the feasibility of using unlabeled source samples for DG through semi-supervised meta-learning (Sharifi-Noghabi et al., 2020), and subsequent methods have increasingly treated pseudo-label quality, domain-invariant representation learning, and cross-domain regularization as the central technical bottlenecks.

1. Problem formulation and task variants

The common objective in this family is to learn a model from multiple source domains that generalizes to an unseen target domain without access to target-domain data during training. A standard formulation uses source domains $\{\mathcal{D}_i\}_{i=1}^N$, where each domain is partitioned into a small labeled set and a large unlabeled set, and test-time evaluation is performed on an unseen target domain $\mathcal{D}_T$ (Qi et al., 2022). A closely related formulation writes the predictor as $\mathcal{F}=w\circ f$, with $f$ a feature encoder and $w$ a classifier, and assumes a shared label space $y\in\mathcal{Y}=\{1,\dots,C\}$ across domains while the input marginal $\mathcal{P}(\mathcal{X}^d)$ changes by domain (Galappaththige et al., 2024).

Several papers make a sharper distinction between SSDG and CD-SSDG. One setting assumes that only one source domain is labeled and the remaining source domains are entirely unlabeled, with the target domain unseen during training (Wang et al., 2021). Another paper frames SSDG as a representative case of data inequality across domains, again using one labeled source domain together with multiple unlabeled source domains and an unseen test domain (Park et al., 2024). The most explicit contrast appears in DAC, which defines CD-SSDG as a scenario where labeled data come from only one source domain, unlabeled data come from multiple source domains, and there are domain shifts between the labeled source and unlabeled source domains in addition to the shift to the unseen target domain (Song et al., 25 Sep 2025).

This distinction matters because standard SSL typically assumes labeled and unlabeled data are drawn from the same distribution, whereas CD-SSDG explicitly violates that assumption. Conversely, standard DG assumes fully labeled source domains and therefore does not directly address how to exploit unlabeled multi-domain data. A plausible implication is that CD-SSDG should be understood less as a minor variant of SSL or DG than as a setting with its own failure modes, especially pseudo-label noise induced by inter-domain mismatch.

2. Core difficulties: pseudo-label noise, domain interference, and representation bias

A recurring empirical observation is that classical DG methods underperform in SSDG because they cannot exploit unlabeled data effectively, while SSL baselines such as FixMatch are usually stronger but still leave a substantial gap to fully supervised DG training (Galappaththige et al., 2024). FixCLR further reports that methods such as ERM, EntMin, and MeanTeacher are consistently worse than FixMatch on Digits DG, PACS, Office-Home, and Terra Incognita, motivating SSDG methods built on top of SSL rather than classical DG (Son et al., 25 Jun 2025).

The dominant explanation is pseudo-label unreliability under heterogeneous source distributions. In UPLM, the central problem is that confidence-threshold pseudo-labeling becomes brittle because a model can be highly confident yet wrong on out-of-domain inputs, reflecting poor calibration under multi-source unlabeled data (Khan et al., 2024). MultiMatch emphasizes a related phenomenon: shared batch normalization statistics and shared classifiers can introduce interference across domains, harming pseudo-label quality when source distributions differ (Qi et al., 2022). DGWM makes the same point at the classifier level, arguing that when more source domains are added, pseudo-label accuracy drops because a single shared classifier tends to lose domain-specific specialization (Galappaththige et al., 2024).

Several methods connect pseudo-label quality directly to generalization. MultiMatch derives motivation from a multi-domain generalization bound and interprets it as saying that mitigating domain discrepancy and exploiting all samples can reduce generalization error in each source domain and thereby improve pseudo-label accuracy (Qi et al., 2022). DGSML likewise uses entropy-weighted pseudo-labeling and centroid-based regularization so that unlabeled samples only influence class centroids conservatively when predictions are confident (Sharifi-Noghabi et al., 2020). This suggests a common view across the literature: in CD-SSDG, pseudo-labeling is not an auxiliary engineering detail but the main channel through which unlabeled multi-domain data become useful or harmful.

3. Methodological patterns

The literature has converged on several recurring design patterns: pseudo-label refinement, domain-aware modeling, representation-level alignment, multi-view or co-training structures, and explicit domain-invariance regularization.

One line of work improves pseudo-label selection itself. UPLM adds uncertainty-guided pseudo-labeling with Monte-Carlo dropout, requiring both confidence above $\tau$ and certainty above $\eta$ before accepting a pseudo-label; it then applies model averaging at inference using $\theta_{best}$, $\mathcal{D}_T$0, and $\mathcal{D}_T$1 (Khan et al., 2024). The method reports that UPL improves pseudo-label accuracy on PACS from 85.34% to 92.20% on average (Khan et al., 2024). Other methods refine pseudo-labels through feature structure rather than uncertainty alone. The feature-based conformity and semantics alignment approach aligns output-space pseudo-labels with prototype-induced feature-space posteriors and regularizes feature geometry with prototype attraction and repulsion, using the total objective

$\mathcal{D}_T$2

(Galappaththige et al., 2024).

A second line retains domain-specific information during training. DGWM computes a domain information vector from unlabeled minibatch features and uses it to modulate classifier weights on the fly via

$\mathcal{D}_T$3

with the mask generated from the current domain representation (Galappaththige et al., 2024). The stated purpose is to retain domain-level specialism in the classifier while keeping a shared parameterization (Galappaththige et al., 2024). Earlier work on one-labeled-domain SSDG instead used domain-aware prototypes and a domain-aware pseudo-label score

$\mathcal{D}_T$4

combined with a dual-classifier design that separates pseudo-label generation from generalization learning (Wang et al., 2021). ProUD similarly begins with domain-aware prototypes for pseudo-labeling, then uses a prototype merging loss to collapse domain-specific prototypes toward class-level anchors (Park et al., 2024).

A third line explicitly regularizes cross-domain representations. FixCLR is a domain-invariance regularizer layered on top of FixMatch-style SSL. It uses pseudo-labels to form class groups across domains but removes positive attraction entirely, employing a repelling-only contrastive loss

$\mathcal{D}_T$5

with a contrastive term defined to separate different-class samples across all domains (Son et al., 25 Jun 2025). The paper argues that positive attraction is risky because pseudo-label errors can be reinforced, whereas repulsion is more robust under noisy labels (Son et al., 25 Jun 2025).

A fourth pattern uses multi-task or co-training architectures to reduce domain interference. MultiMatch treats each source domain as a local task and all source domains together as a global task, using independent BN and classifier heads for each task while sharing most other parameters (Qi et al., 2022). DAC uses two sub-models with cross pseudo supervision, cross feature supervision, and asymmetric auxiliary tasks, with the overall loss

$\mathcal{D}_T$6

(Song et al., 25 Sep 2025). The explicit rationale is that feature-level supervision is less brittle than pseudo-label supervision under domain shifts between labeled and unlabeled data (Song et al., 25 Sep 2025).

4. Representative formulations and architectural motifs

Different papers instantiate these patterns with distinct but related mathematical structures.

DGSML combines supervised classification, entropy-based pseudo-labeling, a discrepancy loss that keeps class centroids before and after adding pseudo-labeled unlabeled data close,

$\mathcal{D}_T$7

and an alignment loss that preserves relative class-centroid geometry across meta-train and meta-test domains (Sharifi-Noghabi et al., 2020). Its episodic meta-learning procedure repeatedly splits source domains into meta-train and meta-test subsets to mimic train/test domain shift (Sharifi-Noghabi et al., 2020).

MultiMatch extends FixMatch into a multi-task framework with $\mathcal{D}_T$8 local tasks and one global task. During training, pseudo-labels are generated by fusing the local and global predictions,

$\mathcal{D}_T$9

and at test time the global prediction is combined with the most compatible local task via

$\mathcal{F}=w\circ f$0

(Qi et al., 2022). The independent BN formulation,

$\mathcal{F}=w\circ f$1

is used to formalize why shared normalization can inject cross-domain interference (Qi et al., 2022).

ProUD organizes training into Domain-aware Prototype-based Pseudo-labeling, Prototype Merging Loss, and Uncertainty-adaptive Domain Mix. For each domain and class it computes prototypes $\mathcal{F}=w\circ f$2, assigns pseudo-labels by nearest prototype in cosine distance, estimates uncertainty by prototype-based entropy, and learns with

$\mathcal{F}=w\circ f$3

(Park et al., 2024). The uncertainty-adaptive mixing coefficient is made smaller when uncertainty is larger, so less reliable pseudo-labeled samples contribute less strongly to mixed training examples (Park et al., 2024).

DAC formalizes a newer CD-SSDG regime for medical segmentation by mixing original and style-augmented unlabeled images with CutMix, generating cross pseudo-labels between two asymmetric sub-models, and adding feature-level MSE supervision

$\mathcal{F}=w\circ f$4

(Song et al., 25 Sep 2025). It then augments the co-training structure with mixed patch localization and random patch rotation tasks to maintain learner diversity (Song et al., 25 Sep 2025).

A general pattern across these formulations is the combination of a standard SSL backbone with one or more cross-domain regularizers. This suggests that the field increasingly treats strong SSL baselines as the default substrate, while CD-SSDG-specific advances are introduced through auxiliary objectives, domain-aware parameterization, or richer pseudo-label verification mechanisms.

5. Benchmarks, regimes, and empirical patterns

The classification literature largely centers on multi-domain image benchmarks such as PACS, Office-Home, VLCS, DigitsDG, Terra Incognita, miniDomainNet, DomainNet, ImageNet-R, and FMOW-Wilds. MultiMatch evaluates on PACS, Office-Home, and miniDomainNet under 10-label-per-class and 5-label-per-class regimes and reports average accuracies of 81.57%, 62.57%, and 58.79% respectively in the 10-label setting (Qi et al., 2022). The feature-based conformity and semantics alignment method uses leave-one-domain-out evaluation on PACS, OfficeHome, VLCS, DigitsDG, and TerraIncognita, with ImageNet-pretrained ResNet-18 and a single-layer MLP head (Galappaththige et al., 2024). FixCLR expands evaluation to six datasets, including ImageNet-R with 15 domains and FMOW-Wilds with 13 domains, and emphasizes that many-domain datasets had not been explored much in prior SSDG studies (Son et al., 25 Jun 2025).

A recurring empirical pattern is that methods built on SSL baselines outperform classical DG baselines in low-label regimes. FixCLR states that plain FixMatch is already stronger than traditional DG methods in SSDG, and that combinations such as FixCLR + SoftMatch or FixCLR + StyleMatch frequently give the best overall results (Son et al., 25 Jun 2025). DGWM reports average gains over FixMatch of +2.4% for the 5-label setting, +2.1% for the 10-label setting, and about +3.1% in the one-source-fully-labeled setting (Galappaththige et al., 2024). UPLM reports average accuracy gains over FixMatch on PACS, OfficeHome, VLCS, and TerraIncognita, with especially large increases on VLCS and TerraIncognita (Khan et al., 2024). ProUD reports that it outperforms all baselines on average accuracy across PACS, Digits-DG, and Office-Home, while also obtaining low standard deviation across domain combinations (Park et al., 2024).

Medical image segmentation has developed its own CD-SSDG subliterature. AHDC addresses cross-domain semi-supervised left-atrium segmentation using bidirectional adversarial inference and hierarchical dual consistency, reporting, for example, 0.917 DSC / 0.848 JI / 1.17 mm ASD when C1 supports C2 (Chen et al., 2021). DAC evaluates on Fundus, Polyp, and SCGM and reports an average DSC improvement of +10.75% versus EPL for optic cup segmentation under 20% labeled data on Fundus, and +7.93% DSC over EPL on SCGM with 20% labeled data (Song et al., 25 Sep 2025). In cardiac MRI segmentation, a Fourier-augmentation and double-CACPS method reports validation average Dice improvement from 0.547 with DeepLabv3+ to 0.738 with the double CACPS ensemble, and a final test avg-dice of 0.828 on CMRxMotion (Ma et al., 2022).

Object detection has also adopted the paradigm. CDDMSL formulates semi-supervised domain generalization for object detection with one labeled source and one or more unlabeled source domains, leveraging vision-language pre-training and language-space alignment rather than visual-space alignment (Malakouti et al., 2023). It reports 11.7% and 7.5% improvement in DG and DA settings, respectively, and evaluates on VOC/Clipart/Watercolor/Comic and Cityscapes/Foggy-Cityscapes/BDD100K using mAP at IoU 0.5 (Malakouti et al., 2023).

6. Conceptual debates, assumptions, and limitations

The literature contains several explicit points of disagreement or caution. The first concerns whether stronger domain invariance should be enforced by attraction or by repulsion. FixCLR argues that adding same-class attraction hurts performance in SSDG and intentionally uses only a repelling term, because cross-entropy already provides class separation and positive attraction can amplify pseudo-label errors (Son et al., 25 Jun 2025). By contrast, prototype-based methods such as the semantics alignment approach and ProUD do use attraction toward same-class prototypes across or within domains (Galappaththige et al., 2024). This does not amount to a formal contradiction, because the mechanisms differ, but it indicates that the role of attraction depends on how class structure is parameterized and how noisy pseudo-labels are expected to be.

A second debate concerns how much domain-specific information should be preserved during training. DGWM explicitly argues that a shared classifier should not be forced to be completely domain-agnostic during training, and instead introduces on-the-fly domain-aware weight modulation (Galappaththige et al., 2024). MultiMatch reaches a related conclusion through independent BN and classifier heads for local tasks (Qi et al., 2022). At the same time, most methods ultimately seek domain-generalizable or domain-invariant features, so the tension is not between specialization and invariance per se, but between temporary domain-aware computation and the final requirement of unseen-domain generalization.

Several assumptions recur. Most methods assume a shared class space across domains (Galappaththige et al., 2024). Many require known source-domain identities in order to build local tasks, domain-specific prototypes, or domain information vectors (Qi et al., 2022). Some methods are designed for fixed classes and fixed domain structure rather than evolving domains or label spaces (Son et al., 25 Jun 2025). In medical imaging, some approaches assume sufficient structural relatedness across domains for alignment or consistency learning to remain meaningful (Chen et al., 2021).

Limitations are also consistent across papers. Dependence on pseudo-label quality remains fundamental: noisy pseudo-labels can still propagate errors, especially early in training or under severe domain shift (Khan et al., 2024). Conservative filtering may improve pseudo-label accuracy at the cost of using fewer unlabeled samples, producing a quality–quantity trade-off (Son et al., 25 Jun 2025). Pretraining can strongly affect results and fairness of comparison, especially when ImageNet-pretrained backbones are used on visually similar data (Son et al., 25 Jun 2025). Computational overhead can increase when methods rely on Monte-Carlo dropout, style synthesis, extra prototype computation, or multiple model branches, although several papers emphasize plug-and-play designs with modest additional cost (Khan et al., 2024).

These patterns suggest that CD-SSDG has matured into a distinct research area defined less by a single canonical architecture than by a shared optimization problem: how to exploit unlabeled cross-domain data without allowing domain shift to corrupt the supervisory signal.

7. Relation to adjacent paradigms and current trajectory

CD-SSDG is closely related to DG, SSL, domain adaptation, semi-supervised segmentation, and self-supervised representation learning, but it differs from each in a specific way. Relative to DG, it replaces the assumption of fully labeled source domains with limited labeled data and much larger unlabeled pools (Qi et al., 2022). Relative to SSL, it relaxes the i.i.d. assumption between labeled and unlabeled data by allowing domain-shifted unlabeled sources (Khan et al., 2024). Relative to domain adaptation, it forbids access to the target domain during training and instead uses multiple source domains to prepare for an unseen test distribution (Park et al., 2024). Relative to standard co-training or consistency learning, it must account for both pseudo-label uncertainty and cross-domain mismatch (Song et al., 25 Sep 2025).

The field’s recent trajectory is toward stronger and more explicit cross-domain regularization. Early methods such as DGSML centered on episodic meta-learning and centroid alignment (Sharifi-Noghabi et al., 2020). Subsequent work moved toward domain-aware pseudo-label correction, multi-task prediction fusion, and prototype-based feature regularization (Wang et al., 2021). More recent methods increasingly treat SSL backbones as fixed infrastructure and focus on add-on modules: uncertainty filtering and model averaging, feature-space conformity losses, prototype merging, weight modulation, negative-class contrastive regularization, and dual-supervised asymmetric co-training (Khan et al., 2024).

A plausible implication is that the next stage of the area will continue to refine the interface between pseudo-labeling and domain invariance rather than abandon either component. Within the available literature, the most stable conclusion is that CD-SSDG performance depends on jointly controlling three quantities: the correctness of unlabeled supervision, the degree of domain interference in intermediate representations, and the extent to which class semantics remain consistent across domains.