Learning Adaptive Distribution Alignment with Neural Characteristic Function for Graph Domain Adaptation

Graph Domain Adaptation (GDA) transfers knowledge from labeled source graphs to unlabeled target graphs but is challenged by complex, multi-faceted distributional shifts. Existing methods attempt to reduce distributional shifts by aligning manually selected graph elements (e.g., node attributes or structural statistics), which typically require manually designed graph filters to extract relevant features before alignment. However, such approaches are inflexible: they rely on scenario-specific heuristics, and struggle when dominant discrepancies vary across transfer scenarios. To address these limitations, we propose \textbf{ADAlign}, an Adaptive Distribution Alignment framework for GDA. Unlike heuristic methods, ADAlign requires no manual specification of alignment criteria. It automatically identifies the most relevant discrepancies in each transfer and aligns them jointly, capturing the interplay between attributes, structures, and their dependencies. This makes ADAlign flexible, scenario-aware, and robust to diverse and dynamically evolving shifts. To enable this adaptivity, we introduce the Neural Spectral Discrepancy (NSD), a theoretically principled parametric distance that provides a unified view of cross-graph shifts. NSD leverages neural characteristic function in the spectral domain to encode feature-structure dependencies of all orders, while a learnable frequency sampler adaptively emphasizes the most informative spectral components for each task via minimax paradigm. Extensive experiments on 10 datasets and 16 transfer tasks show that ADAlign not only outperforms state-of-the-art baselines but also achieves efficiency gains with lower memory usage and faster training.

Learning Structure-Semantic Evolution Trajectories for Graph Domain Adaptation

Graph Domain Adaptation (GDA) aims to bridge distribution shifts between domains by transferring knowledge from well-labeled source graphs to given unlabeled target graphs. One promising recent approach addresses graph transfer by discretizing the adaptation process, typically through the construction of intermediate graphs or stepwise alignment procedures. However, such discrete strategies often fail in real-world scenarios, where graph structures evolve continuously and nonlinearly, making it difficult for fixed-step alignment to approximate the actual transformation process. To address these limitations, we propose \textbf{DiffGDA}, a \textbf{Diff}usion-based \textbf{GDA} method that models the domain adaptation process as a continuous-time generative process. We formulate the evolution from source to target graphs using stochastic differential equations (SDEs), enabling the joint modeling of structural and semantic transitions. To guide this evolution, a domain-aware network is introduced to steer the generative process toward the target domain, encouraging the diffusion trajectory to follow an optimal adaptation path. We theoretically show that the diffusion process converges to the optimal solution bridging the source and target domains in the latent space. Extensive experiments on 14 graph transfer tasks across 8 real-world datasets demonstrate DiffGDA consistently outperforms state-of-the-art baselines.