Generalized Class Discovery (GCD) clusters base and novel classes in a target domain, using supervision from a source domain with only base classes. Current methods often falter with distribution shifts and typically require access to target data during training, which can sometimes be impractical. To address this issue, we introduce the novel paradigm of Domain Generalization in GCD (DG-GCD), where only source data is available for training, while the target domain—with a distinct data distribution—remains unseen until inference. To this end, our solution, DG2CD-Net, aims to construct a domain-independent, discriminative embedding space for GCD. The core innovation is an episodic training strategy that enhances cross-domain generalization by adapting a base model on tasks derived from source and synthetic domains generated by a foundation model. Each episode focuses on a cross-domain GCD task, diversifying task setups over episodes and combining openset domain adaptation with a novel margin loss and representation learning for optimizing the feature space progressively. To capture the effects of fine-tunings on the base model, we extend task arithmetic by adaptively weighting the local task vectors concerning the fine-tuned models based on their GCD performance on a validation distribution. This episodic update mechanism boosts the adaptability of the base model to unseen targets. Experiments across three datasets confirm that DG2CD-Net outperforms existing GCD methods customized for DG-GCD.

Generalized Category Discovery (GCD) aims to classify test-time samples into either seen categories—available during training—or novel ones, without relying on label supervision. Most existing GCD methods assume simultaneous access to labeled and unlabeled data during training and arising from the same domain, limiting applicability in open-world scenarios involving distribution shifts. Domain Generalization with GCD (DG-GCD) lifts this constraint by requiring models to generalize to unseen domains containing novel categories, without accessing target-domain data during training. The only prior DG-GCD method, DG$^2$CD-Net~\cite{dg2net}, relies on episodic training with multiple synthetic domains and task vector aggregation, incurring high computational cost and error accumulation. We propose \textsc{HiDISC}, a hyperbolic representation learning framework that achieves domain and category-level generalization without episodic simulation. To expose the model to minimal but diverse domain variations, we augment the source domain using GPT-guided diffusion, avoiding overfitting while maintaining efficiency. To structure the representation space, we introduce \emph{Tangent CutMix}, a curvature-aware interpolation that synthesizes pseudo-novel samples in tangent space, preserving manifold consistency. A unified loss—combining penalized Busemann alignment, hybrid hyperbolic contrastive regularization, and adaptive outlier repulsion—facilitates compact, semantically structured embeddings. A learnable curvature parameter further adapts the geometry to dataset complexity. \textsc{HiDISC} achieves state-of-the-art results on PACS~\cite{pacs}, Office-Home~\cite{officehome}, and DomainNet~\cite{domainnet}, consistently outperforming the existing Euclidean and hyperbolic (DG)-GCD baselines.