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Learning Structure-Semantic Evolution Trajectories for Graph Domain Adaptation

Wei Chen, Xingyu Guo, Shuang Li, Yan Zhong, Zhao Zhang, Fuzhen Zhuang, Hongrui Liu, Libang Zhang, Guo Ye, Huimei He

TL;DR

DiffGDA reframes Graph Domain Adaptation as a continuous-time diffusion process that evolves structure and semantics from a labeled source graph to an unlabeled target graph. It combines forward diffusion of augmented features with a domain-aware reverse diffusion guided by a density-ratio signal, and proves convergence to an optimal adaptation path in latent space. Empirically, it achieves state-of-the-art performance across 14 transfer tasks on 8 real datasets, while maintaining practical efficiency through targeted diffusion and end-to-end training. This diffusion-based approach provides a flexible, scalable solution for nonlinear and heterogeneous graph shifts in real-world applications.

Abstract

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.

Learning Structure-Semantic Evolution Trajectories for Graph Domain Adaptation

TL;DR

DiffGDA reframes Graph Domain Adaptation as a continuous-time diffusion process that evolves structure and semantics from a labeled source graph to an unlabeled target graph. It combines forward diffusion of augmented features with a domain-aware reverse diffusion guided by a density-ratio signal, and proves convergence to an optimal adaptation path in latent space. Empirically, it achieves state-of-the-art performance across 14 transfer tasks on 8 real datasets, while maintaining practical efficiency through targeted diffusion and end-to-end training. This diffusion-based approach provides a flexible, scalable solution for nonlinear and heterogeneous graph shifts in real-world applications.

Abstract

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.
Paper Structure (31 sections, 1 theorem, 28 equations, 9 figures, 5 tables, 1 algorithm)

This paper contains 31 sections, 1 theorem, 28 equations, 9 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Methodology
  5. Domain-Guided Graph Diffusion Process
  6. Practical Implementation
  7. Experiments
  8. Experimental Setup
  9. Main Experimental Results (RQ1)
  10. Ablation Studies (RQ2)
  11. Hyper-parameter Analysis (RQ3)
  12. Model Efficiency Analysis (RQ4)
  13. Visualization for Representation Space (RQ5)
  14. Conclusion
  15. Theoretical Proof
  16. ...and 16 more sections

Key Result

Theorem 1

Let $\mathbf{G}^{\mathcal{S}}$ and $\mathbf{G}^{\mathcal{T}}$ denote the source and target graphs, respectively. Suppose the data distributions $p$ and $q$ define the forward diffusion processes on these two domains, respectively. Following ouyangtransfer, the optimal diffusion network $\mathbb{P}({ where the first term is the score function of the source graph, and the second term represents the

Figures (9)

  • Figure 1: Overall architecture of our proposed DiffGDA framework: (1) In the forward diffusion process, labeled source graphs $\mathbf{G}^\mathcal{S}$ are progressively perturbed with noise, approximating a Gaussian distribution. (2) During the reverse diffusion process, a guidance network aligns predicted and true density ratios, reconstructing intermediate graphs to match the target distribution. The generated labeled graphs are then utilized for node classification training with a GNN.
  • Figure 2: Classification Mi-F1 comparisons between DiffGDA variants on four cross-domain tasks.
  • Figure 3: The performances of our DiffGDA w.r.t varying $\alpha$, $\eta$ and $\mathsf{T}$ on different transfer tasks.
  • Figure 3: Runtime (seconds) and Mi-F1 ($\%$) comparison on two transfer tasks. All models are trained using a single RTX 4090 GPU.
  • Figure 4: The training curves of Mi-F1 scores on three baselines across two cross-domain transfer scenarios over 150 epochs.
  • ...and 4 more figures

Theorems & Definitions (1)

  • Theorem 1