Learning Structure-Semantic Evolution Trajectories for Graph Domain Adaptation
Authors: Wei Chen
Xingyu Guo
Shuang Li
Yan Zhong
Zhao Zhang
Fuzhen Zhuang
Hongrui Liu
Libang Zhang
Guo Ye
HUIMEI HE
Venue: ICLR 2026 Poster (2026)
Keywords: Graph Domain Adaptation
Stochastic Differential Equations
Primary area: learning on graphs and other geometries & topologies

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.

Published as a conference paper at ICLR 2026
LEARNING STRUCTURE-SEMANTC EVOLUTION TRA- JECTORIES FOR GRAPH DOMAIN ADAPTATION
Wei Chen',
Xingyu Guo',
Shuang Li',
Yan Zhong',
Zhao Zhang',
Fuzhen thuang!At, Hongrui Liu Libang Zhang',
Guo Ye,,
Huimei He
'School of Artificial Intelligence, Beihang University, Beijing, China
School of Mathematical Sciences, Peking University, Beijing, China
'School of Computer Science and Engineering, Beihang University, Beijing, China
"Zhongguaneun Laboratory. Beijng. China $ 'Independent Researcher, Beijing, China (chenwel Somnwei23, 123, shuangl i aai, zhuangfuzhen] (eterezeeeeeeaaaaaaaaaaa @buaa abweeeeddaaaaaa...... edu..cn
ABSTRACT
Graph Domain Adaptation (GDA) aims to bridge distribution shifts between do- mains by transferring knowledge from well-labeled source graphs to given unla- beled target graphs. One promising recent approach addresses graph transfer by discretizing the adaptation process, typically through the construction of interme- diate 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 ac- tual transformation process. To address these limitations, we propose DifTGDA a Diffusion- 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, domain- aware network is introduced to steer the generative process toward the target do- main, 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 14 graph transfer tasks across 8 real-world datasets demonstrate DifiGDA con- sistently outperforms state-of-the-arr baselines. Code is available at DiÉÉGDA.
INTRODUCTION
Graph Neural Networks (GNNs) (Zhu et al., 2021; Wu et al., 2022) have demonstrated remarkable success in various real-world applications (Zhang al., 2022a; Therrien et al., 2025; Chen al., 2024; 2025b). However, their performance often degrades under distribution shifts across training and testing graphs (Liu al., 2020; Qin et al., 2022). To overcome this limitation, Graph Domain Adaptation (GDA) aims to transfer knowledge from a labeled source graph to an unlabeled target graph by mitigating both feature distribution discrepancy and structural divergence (Dai al., 2022; Liu et al., 2024a; Chen et al., 2025a). This work focuses node-level GDA (Ding et al., 2018; Wang et al., 2024), tackling critical challenges posed by feature and topological shifts across graphs.
In recent years, wide range of methods have emerged to enhance GDA, which can be broadly categorized into two paradigms (Huang et al., 2024): (1) Model-oriented approaches (Xiao et al., 2023; Pilanci & Vural, 2020; Dan et al., 2024; Fang et al., 2025b) aim to learn domain-invariant rep- resentations by aligning both semantic and structural information through objectives such as mini- mizing subgraph structural distances (Liu et al., 2023a; You et al., 2023), reducing Maximum Mean Discrepancy (MMD) (Chen et al., 2019; 2025a), and using adversarial discriminators (Dai et al,, 2022). While these methods promote representation sharing, they assume limited structural vari- ation between domains, which restricts their effectiveness when substantial structural differences exist (Huang al., 2024). (2) Data-oriented methods (Na al., 2021; Huang al., 2024; Lei
'Corresponding author.

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et al., 2025) address these challenges by constructing intermediate graphs bridge structural gaps, projecting both domains into a shared semantic space. This facilitates more stable training by align- ing structures and capturing coss-graph correspondences, offering more flexible and interpretable framework for GDA, and showing promising potential in tackling complex graph domain shifts.
However, most data-oriented methods rely the assumption that the graph transfer process is dis- crete, meaning the source graph can be transformed into the target graph through a limited number of alignment steps. Unfortunately, this assumption often fails in real-world scenarios, particularly when dealing with unlabeled graphs, due to the key limitations: graphs are governed by different underlying processes (Deng et al., 2019; Sharma et al., 2024), such as social dynamics, citation growth, or knowledge diffusion, which evolve nonlinearly and in domain lution is driven by complex, context-dependent dynamics, rather than fixed or proportional struc- tural patterns. Additionally, semantic information arises from the interplay between node features and structural context, but it often lacks explicit anchors for alignment (Heimann et al., 2018; Zhao et al., 2023). These factors make it difficult to align graphs with fixed number of steps, as structural and semantic differences cannot be effectively bridged through simple alignment processes.
ways. Their evo-
Along this research line, continuous evolution (Zeng et al., 2024; Zhang et al., 2021) provides more natural modeling paradigm for graph transfer. Rather than manually constructing discrete in- termediate graphs, this approach directly models the underlying evolution process, where the source graph gradually transforms into the target graph over continuous time. This paradigm not only by- passes the limitations of step-by-step alignment but also offers several advantages for GDA: (1) Structural changes are represented as smooth temporal trajectories, enabling flexible adaptation to nonlinear and heterogeneous topologies without relying on rigid graph (or subgraph) level align- ment. (2) Semantic information evolves continuously along the transformation path, allowing the model automatically learn optimal alignment trajectories and establish accurate cross-domain cor- respondences in an end-to-end manner. This perspective motivates generative view of GDA, where the transfer of structure and semantics is unified as a time-driven evolutionary process. Inspired by the success of diffusion models in capturing complex distributional transformations (Croitoru et al., 2023; Zeng et al., 2024), we adopt a stochastic differential equation (SDE) (Protter, 2012; Li et al., 2020) framework to represent cross-graph transfer a continuous probabilistic flow.
In this work, we propose DIfTGDA, a Diffusion adaptation as a continuous tie evolution process. To guide this evolution, we introduce domain- aware network that learns to steer the generative trajectory toward the target domain by uncovering the optimal adaptation path. This adaptive guidance allows the model to overcome the limitations of conventional discrete alignment methods by continuously directing the evolution toward the target domain, resulting in more coherent structural alignment and semantic adaptation. Furthermore, provide a theoretical guarantee that the guided diffusion process converges to an optimal adaptation trajectory, effectively bridging the source and target domains.
GDA that models both structural and semantic
Overall, our contributions can be summarized as:
() Continuous Evolution Modeling. We formulate GDA continuous-time generative pro- cess, jointly capturing structural and semantic transitions via stochastic differential equations. To the best of our knowledge, DiffGDA is the first work that brings diffusion into GDA. (ii) Domain- Aware Guidance Network. We propose density-ratio-ban based guidance mechanism that adaptively steers the diffusion trajectory, enabling precise, target-aware evolution. (iii) Empirical Superior- ity. Extensive experiments on 14 real-world transferring tasks demonstrate the effectiveness of the proposed DifIGDA, consistently outperforming state-of-the-art baselines.
2 RELATED WORK
Graph Domain Adaptation (GDA) has attracted significant research attention due to its crucial role in enabling knowledge transfer between graphs with distributional shifts (Ding et al., 2018; Zhang et al., 2022b; Liu et al., 2023a; 2024a; Chen et al., 2025a; Guo et al., 2025; Kou et al., 2025b;a), Early approaches (Zhang et al., 2019; Wu et al., 2020; Dai et al., 2022; Pilancı & Vural, 2020; Dan et al., 2024) primarily adopted model- paradigm, focusing on learning tations through techniques like adversarial training and MMD minimization (Liu et al., 2024a; You al., 2023). While effective, these methods often struggle due to their reliance rigid parametric
represen-
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frameworks, which impose inherent limitations their performance. Recently, data-driven meth- ods (Huang et al., 2024; Lei et al., 2025) have emerged as a promising alternative, addressing domain gaps through intermediate graph construction and transformation. However, these approaches typ- ically rely on heuristic alignment rules, which often lack generality and cannot adaptively discover or generate intermediate graphs that best suit the structural and semantic characteristics of the graph data, thereby limiting their effectiveness in handling complex graph domain transitions.
Graph Diffusion Models. Diffusion models (Cao et al., 2024) have achieved significant success across a variety of domains (Kong et al., 2021; Saharia et al., 2022; Luo et al., 2024b; Zhang et al., 2025: Chen et al., 2025c). In graph domain, these models are increasingly applied to model complex graph-structured data, particularly for tasks such as node and edge generation, molecule creation, and protein design (Niu al., 2020; Jo et al., 2022; Konstantin Haefeli et al., 2022). By carefully designing the noising process and model architectures, symmetry constraints on the transition ker- nel and prior distribution can be explicitly incorporated, ensuring that the generated data follows roto-translationally invariant distributions. Recent advancements have expanded these frameworks beyond score-based formulations, introducing techniques like flow matching (Lipman et al., 2023; Liu et al., 2023b) and optimal transport-based diffusion (Peyré et al., 2019). These approaches pro- vide alternative mechanisms to enforce geometric and permutation symmetry constraints in graph generation tasks. However, most existing methods have focused on symmetric diffusion processes. This presents a key challenge for diffusion-basee domain adaptation models: how to leverage asym- metric diffusion mechanisms to enable transfer learning across heterogeneous graphs
3 PRELIMINARIES
Notation. Given a labeled source graph G = (ys,Es) where Vs is the set of nodes, gs C ys x VS is the set of edges, and the nodes y are associated with feature matrix X E R and a label matrix YS E {0, 1. The adjacency matrix of the source graph is denoted as A E {0, l NsNNs Similarly, we have an unlabeled target graph GT = (V", G features X E N and adjacency matrix A" E {0, 1J feature space (F (F-dimensional) and label space (C classes), but they exhibit domain shift. In this work, our goal is to train GNN that accurately predicts the node labels of the target graph GT.
,TT) with node
Both graphs share the same
Diffusion Models. Diffusson models (Croitoru et al., 2023; Cao et al., 2024) have emerged as leading generative techniques in various fields (Luo et al., 2024b; Kong et al., 2021; Liu et al., 2025). These models are built upon the concept of a diffusion process that gradually transforms data into noise and then trains models reverse this process using a well-defined objective func- tion. Formally, the forward process incrementally corrupts data Xo ~ p(Xo) into noise through a continuous-time stochastic differential equation (SDE) (Protter, 2012):
dX,- f(X,, t)dt + g()dd,, E [),
(I)
where w. denotes the standard Brownian motion (also called the Wiener process) (Luo et al., 2024a), f(X,,t): : Rd [0, T] + Rd is vector-valued drift coefficient determining the deterministic evolu- tion of the system, and g(t [0, T] + IR is scalar diffusion coefficient controlling the magnitude of Gaussian noise added at each time step. A canonical example is the Somstein-Ullenbee
process
(Maller et al., 2009), where f(X,,t) t) = - 1 Xt)x, and g(t) = / /3()). with (() being a noise schedule that determines the rate of data corruption. As t - T, the distribution pa (X.) converges to a simple prior distribution (typically standard Gaussian), regardless of the initial data distribution Po (Xo). The reverse process aims to invert this corruption using the reverse-timg SDE:
dx,- f(X.,t) Vx) logpe (X.) di g(()dw,,
where Vx, log Pe (X,,) denotes score function, di is an infinitesimal negative time step, and w; is the reverse-time Brownian motion (Freedman, 2012). The score function is approximated by neural network trained via score matching (Kane et al., 2020), which minimizes the Fisher divergence between the model and the true data distribution to ensure accurate and data-consistent generation.
4 METHODOLOGY
In this section, we present the DifIGDA framework (Figure 1). We first introduce $4.1 Domain- Guided Graph Diffusion, which formulates adaptation continuous-time evolution. We then de-
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Forward Diffiusion Process
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X3
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Overall architecture of our proposed DifIGDA framework: (1) In the forward diffusion process, labeled source graphs G 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 GNN.
Figure 1:
scribe $4.2 Practical Implementation, covering the design of score and guidance networks, Finally, we detail the model optimization that integrates diffusion with GNN for end-to end-to-end training.
4.1 DOMAIN-GUIDER GRAPH DIFFUSION PROCESS
Forward Diffusion Process. DifiGDA formulates GDA as continuous-tin time stochastic process, governed by system of SDEs. For source graph denoted G (X A YS), we design forward diffusion process that systematically perturbs both node features and adjacency matrices toward a tractable noise distribution. To integrate the source domain label knowledge into the dif- fusion process, we propose a structured feature concatenation to explicitly establish the semantic association between node features and labels. Specifically, the original node feature matrix X and the label matrix Y are concatenated along the channel dimension to construct augmented features: X |X||| R (F++FC), where denotes the concatenation operation.
Formally. this process is defined as a continuous-ting time stochastic trajectory {G.
(X:5 A A over a fixed temporal domain [0, T], where G represents the initial source graph. The complete dynamics of the forward process governed by the following SDE:
5 = fe fG )t + g. (G ddw,
(3)
where f, governs the deterministic drift, 9r controls the noise injection rate. The Wiener process w drives the stochastic component. Overall, this process transforms the initial graph structure G (XS A into simple noise distribution through designed drift term f, and noise term g.
The reverse diffusion process aims to generate graphs that adhere to the target data distribution. It begins by sampling from the prior distribution and traversing the diffusion process of Eq. (3) backward in time. This reverse process is formulated as:
Reverse Diffusion Process.
dG [r.(G)) V log pr )G grdw.
where Pt denotes the marginal distribution under the forward diffusion process time is reverse-time standard Wiener process, and dł represents an infinitesimal negative time step.
The key reverse process is estimating the score function Vas log (Gg"). Typically, we can train a neural network P(E) via score matching to approximate this score function (Ouyang et al., 2024), thereby facilitating discrete-time generation via Eq. (4). However, this unconditional generation process only reconstructs the source graph distribution. In our scenario, the objective is to generate graphs conforming to predefined target graph distribution GT, which differs from the source distribution G To address this issue, we propose an additional auxiliary guidance network (()), which steers generation process from the source distribution toward target distribution. Therefore,
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the optimization objective in reverse process is expressed as:
CSDE F (P(E), VGg lo (G: +F (Q(()) +
(G; + G())
(5)
where -): denotes a generic supervised loss (i.e., mean squared error), with the first argument as the trainable predictor and the second argument as its supervision signal. Crucially, (G + Gt") acts as guidance potential, whose gradient a V explicitly encourages alignment with the target domain. Building on the insights from Theorem I, we can deduce the specific v (G, + G
Theorem 1. Let G and G" denote the source and target graphs. respectively. Suppose the data distributions p and q define the forward diffusion processes on these two domains, respectively. Fol- lowing (Ouyang et al., 2024), the optimal diffusion network ((()), for the target graph GT satisfies:
P(()) Va log..((C (G.) (++)+ Va log P )/v(GE))
(6)
where the first term is the score function of the source graph, and the second term represents the gradient of the density ratio between the target and source graph distributions. The density ratio is defined as the likelihood ratio between the target and source domains in the latent space.
Proof: For a detailed derivation, please refer to the Appendix A.I.
Consequently, the optimization objective in Eq. (5) can be rewritten as:
CSDE = F (())) V log (G.)) + ((((), V V log Enceiae (
(7)
The theorem demonstrates that our guidance network adaptively learns the optimal transformation path, directing the generative trajectory toward the target domain. This adaptive guidance enables the model to overcome the limitations of traditional discrete aligmment methods by progressively steering the evolution toward the target domain, resulting in more coherent graph adaptation.
4.2 PRACTICAL IMPLEMENTATION
Optimizing Score Network P(E). To fit the score network, we first need to estimate the score func- tion VGs (G²) (RNxx(F+C) x R.NxNNs, where Ns represents the node number in source graph, F denotes the feature dimensionality, and C' corresponds the class number. However, directly estimating this score function is computationally prohibitive due to the high dimensional- ity of the problem. Thus, we adopt the reverse-time diffusion process (Jo et al., 2022), which is mathematically equivalent to the formulation in Eq. (4) and is modeled by the following SDEs:
ax: = (f) oî. V x log Pa ( A
{ dř + I1.t dw1,
(8)
dA (A,)(A)) 93, V
A log Pt A dī + 92,t dW,,
where fi, and fe.: are linear drift coefficients satisfying f (X, A) = (X), (A). 91,t and g2, are scalar diffusion coefficients, and Wi, W2 represent reverse-time standard Wiener processes. This formulation effectively decomposes the original high-dimensional score function into two partial score functions: V x J. (X: A and VA log P: (X, A.) By splitting the computation, the reduces the complexity of estimating the high-dimensional
problem becomes more tractable, score function into manageable components, which can be estimated using the Variance Exploding (VE) (Yang et al., 2023) technique compute these two gradients. Consequently, the score network P()) is also divided into two parts: P(() & (P(2)) where P((1) is responsible for computing the score function associated with the node features, and P((z) is tasked with computing the score function for the graph adjacency structure, "A" denotes decomposition. To model these two score functions, we utilize two independent multilayer perceptron (MLP) networks:
p(()) = MIP (2)), P(G)) = MLP ([(GMH(H, A
(9)
where AT denotes the higher-order adjacency matrices, and H = GNN(H, A.) with H, = X the input. The GMH refers the graph meati-head attention block, K is the number of GMH
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layers, and L is the number of GNN layers. To approximate these score functions using score network P(C), we define the following training objectives for nodes and edges, respectively:
f arg min Eg λ . M Eos Gg
[|((e)) Vxş log
||
4
(10)
E = arg min Ey 22 og o ((2) - VAy log (A. ||
where A and 22,r are weighting functions and is uniformly sampled from [0, TJ. the E can be efficiently computed using the Monte Carlo estimate (McCool, 1999) with the samples (t, Go. G.).
Optimizing Guidance Network (o). We begin by formulating the gradient estimation objective
VG log EpGs ( y ( ) 3/pp G This objective can be decomposed into two key components:
(1) the density ratio q( ((G)) ((G between target and source domains, and (2) the expectation op- erator over the posterior distribution [G) To address the intractability of direct computation, estimate these two items respectively through the following methods inspired by (Ouyang al., 2024): (1) We approximate the density ratio through domain discrimination. A graph neural classi- fier Caun G UGT y is trained distinguish between source and target domain nodes, using subset of nodes from each domain. Let yx) E [0, 1J denote the classifier's 's output indicating source membership. The density ratio can then be estimated as: g(G) /ppl))p(GBBB
(1 yxx))/y(x). (2) We compute the term Ep(GS GT) (G]) ( using Monte Carlo sampling. This process involves generating multiple perturbed graph instances from the joint distribution p( p(G. G and then av- eraging the computed gradients across these samples (Lu et al., 2023). We approximate the true gradient by sampling from this distribution. The sampling details are provided in Appendix B.
Similarly to the score network P()). we approximate the guidance function using parameterized network (()), where (()) & (Q(o)), Q()2)). Here, Q(61) acts as the domain estimator for node-
level features, while ((d2) serves as the domain estimator for the adjacency matrix. The two com-
ponents are formally expressed as follows:
Q ( = MLP tt. Q(62) = MLP (A
(11)
Thus, the final learning objective for the guidance network Q(6) be described as follows:
6 = arg min E (PGGs.G))) [[))) ((03))))((X/xxx))))))
$1
(12)
55 = arg min E p .ff [[())) ((3))))((AA))//))
82
In this manner, we can achieve an accurate estimation of the guiding function in Eq. (7) as:
((²') (Q(6)), Q(5;)) log E. B (
(13)
The detailed proof can be found in Appendix A.2.
Applying diffusion indiscriminately to all nodes is computationally costly and may weaken infor- mative signals. To mitigate this, we adopt targeted stochastic diffusion strategy that selectively perturbs subset of nodes while keeping the rest intact, i.e., p p(G?) p(G"). A hyperparameter a controls the diffusion ratio, balancing efficiency and information preservation.
Training on Generated Graph G'. After training the diffusion model, we obtain G' (X', A', Y') with node features, adjacency matrix, and labels. Since G' may still differ from the target graph, we adopt an additional MMD aligmment (Huang et al., 2024). The training loss is:
LUNN = (GNN( A'), Y') + y LAMD (GNN(X', ,'). GNN(X AT)),
(14)
where LCE is the cross-entropy loss, LMMD aligns G' with GT, and r is a weighting factor.
The design of G' generation offers two main advantages in GDA. First, it allows the diffusion model to learn class-aware dynamics directly in the joint feature- label space, rather than aligning feature- level distributions alone, which can be ambiguous without labels. Second, by reconstructing labels with features, the model can better capture the relationship between node attributes, structure, and class membership, leading improved node classification performance on the target domain.

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47.08
88.801171
48.07
38.58
40.94.2
47.00
62. 63.80
02. 12.46
51.07
TDSS (AMAL225)
07.43u
63:36aua
30.00am
48.17.:0
47.62
47
36.45
46.0
36.55
36.30aas
45.27 50/73amm
49.24
DGSIDA (CMEE25)
61/7ica
19.50um
48
31.91mm
53.251a
47.581mm
00 10.s5
50 9//00
57.28
(CLR
6L/8912
30.2513e
S1.70asst
30.16.331
32500.57
50.18:10
42.76ane1
48.70.331
47:17::
56.07a1.0
50.3412m
51,98
DIIGDA (Our))
71.76...
12.21
24.18
31.88.m
34.37
20.37
27.18
56.30
32.9 94811u
74.84
60.75
Table I:
Node classification performance (% + σ) on the Citation and Airport domains. The highest scores are highlighted in bold, while the aecond-highes scores are underlined.
Model Optimization. Overall, the objective consists of optimizing both GNN and diffusion model in an end-to-end manner. Specifically, the optimization problem can be formulated as:
min & Eo 11,
CSDE + LONN:
(15)
where l2, 81, 82 represent the diffusion parameters, and & denotes the parameters of the GNN.
Complexity Analysis. The overall computational complexity of DiffGDA is governed by two main components: the diffusion model and the graph neural network (GNN). For the diffusion model, which implemented as multilayer perceptron (MLP), the complexity is O(T n²), where T denotes the number of diffusion steps and n is diffusion node number. Importantly, the targeted diffusion strategy controls n = a|Ds), making a the key knob to balance efficiency. The GNN introduces a complexity of O(L (DDS) + 11))),, where L is the number of layers, | is the number of source nodes, and | is the number of edges in source graph. Thus, the total complexity is O(T n² + L. (DD5+ + (
()). The error bound analysis is provided in Appendix C.
Remark. (Discussion on Computational Cost) Firstly, despite being diffusion- based, our framework introduces stochastic diffusion strategy that processes subsets of nodes while preserving critical source information. With an adjustable sampling ratio, it balances computational cost and perfor- mance, achieving faster convergence and higher accuracy compared to other methods. Secondly, the model complexity is O(T n² + L- -[DV) + 1E))), where T is the diffusion steps, n the sampled nodes, and L the GNN layers. In practice, T < 100 and n is controlled via stochastic sampling. keeping n² manageable. The shallow GNNs further enhance efficiency. Thus, DiffGDA achieves competitive performance with modest computational resources, making practical and efficient.
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Domain
# Datasets
# Nodes
Eddees
# Feat Dims
Labels
ACMv9 (A)
9,360
31,112
Citation
Citationv (C)
8,935
30,196
6,775
5
DBLPv7 (D)
5.484
16,234
USA (U)
1,190
27.198
Airport
Brazil (B)
131
2,148
241
4
Europe (E)
399
11,990
Blog1 (B1)
2,300
66,942
Social
8,189
Blog2 (B2)
2,896
107,672
Table 2: Statistics of the eight real-world datasets.
EXPERIMENTS
In this section, we empirically evaluate the DilIGDA framework through experiments addressing five key research questions: RQ1: How does DiffGDA compare to state-of-the-an methods? RQ2: Which part of the DiffGDA model majorly contributed the effective prediction? RQ3: How do key parameters impact model performance? RQ4: What are the computational efficiency and resource overhead of DifIGDA? RQ5: How can we intuitively understand DiffGDA's strengths?
5.1 EXPERIMENTAL SETUP
(1) Datasets. We employ three domains, as detailed in Table 2, which include a total of eight com- monly used datasets: Citation (ACMv9, Citationvl, DBLPv7) (Dai al., 2022), Airport (USA, Brazil, Europe) (Ribeiro et al., 2017), and Social (Blog Blog2) (Liu et al., 2024a). (2) Baselines. To validate the effectiveness of model, we compare against categories of baseline methods: (1) source-only graph neural networks including GAT, GIN and GCN, which are trained exclusively on the source domain and directly transferred the target domain; and (2) graph domain adapta- tion methods: DANE, UDAGCN, AdaGCN, StruRW, GRADE, PairAlign, GraphAlign, A2GNN, GGDA, TDSS, DGSDA and GAA. The complete experimental setup is provided Appendix D.
5.2 MAIN EXPERIMENTAL RESULTS (RQ1)
We evaluate the performance of DiffGDA framework on node classification tasks across three do- mains, as shown in Table 1 (with additional Social results in Appendix E. The results consistently demonstrate that DiffGDA outperforms state-of-the-art baselines across a variety transfer scenar- ios. On the first three datasets, DiffGDA achieves the highest average score, showcasing its superior- ity in modeling complex cross-domain transitions via continuous time diffusion processes. Unlike traditional discrete intermediate approaches (i.e., GGDA, GraphAlign), DifíGDA effectively cap- tures nonlinear and multi-scale structural discrepancies. Likewise, in the USA, Brazil, and Europe transfer settings, DiffGDA maintains strong generalization capability, significantly outperforming competitive methods such as GraphAlign and TDSS. These findings validate the efficacy our generative continuous evolution perspective, which reduces information distortion and enhances structural alignment in GDA. The significance tests (p < 0.05) are provided in Appendix E.2.
5.3 ABLATION STUDIES (RQ2)
26
ao Model
D22DW WND
CocoFull Mode
To evaluate the contribution of each mod- ule in DiffGDA framework, we con- duct ablation studies on four cross-domain tasks, as shown in Figure 2. Specifically, we investigate the impact of three key components: (i) the domain-aware guid- ance network, which dynamically steers the diffusion trajectory; (ii) MMD align- ment, which matches marginal distribu- tions between domains; and (iii) adjacency constraints, which preserve local structural information during transfer. The results reveal that the full model achieves the best performance across all tasks,
We GuEATTe DEEA'S A4
78
Micrce 19l
Microft 1S4
59
0000 Guidence EEEwi Arj
Mico-FF M9
A-C
C+A
50
B+E
E+00
Figure 2: Classification Mi-F1 comparisons between DiffGDA variants on four cross-domain tasks.
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confirming the effectiveness of integrating all three components. Removing the guidance network leads to substantial drops in performance, especially on the more challenging tasks (e.g., B - E), highlighting its role in maintaining task-relevant diffusion dynamics. MMD alignment has more pronounced effect on simpler shifts such as in A -> C transfer task, where distribution-level match- ing is crucial. 'he removal of adjacency constraints consistently degrades performance, indicating their utility in preserving structural dependencies. Overall, each module plays complementary role: the guidance network stabilizes the diffusion path, MMD facilitates cross-domain alignment, and adjacency constraints reinforce relational structure.
Additional ablation results are provided Appendix E.3.
5.4 HYPER-PARE PARAMETRA ANALYSIS (RQ3)
In this section, we analyze the impact of three key parameters on the proposed DifTGDA framework, as illustrated in Figure the sample ratio a, the loss weight 77, and the diffusion step T.
60
65
-O-
B-U
B-E
A A-C
A A-C
Moro-Ft 1%9)
Micr.FFt (%)
50
81
Moro-Fi (99)
78
Micro-F1
35
21
77
300
20
60
20g
20
60
80
100
61
80
100
0
Miro-F1 (8)
78
D A
Micro-F1 (86)
D-C
Micro-F1 (%)
-A-
U
Moro-F1 (99)
56
U-E
51
53
70
76
51
72
41
20
80
100
Figure 3: The performances of our DifiGDA w.r.t varying a, and T on different transfer tasks.
Study on Sample Ratio The results demonstrate the impact of varying subgraph sampling sizes on the Mi-FI performance across different transfer tasks. For the first two tasks (B - and B - E), the model was evaluated across the full range of sampling sizes (0 ~ 100%) revealing trend where performance initially improves with larger subgraphs, as critical structural information is preserved, but may plateau decline beyond certain point due computational overhead over-smoothing. In contrast, for the latter tasks, the sampling range was truncated to ~ 50% due to out-of-memor issues, indicating that these tasks involve larger or more complex graphs where aggressive subgraph sampling is necessary to maintain feasibility. This aligns with the model's design goal of leveraging liffusion-based generation while managing scalability. Further investigation needed determine the relationship between graph properties and the ideal sampling size.
Study on Loss Weight 7/. We analyze the impact of coefficient r) Eq. (14). As shown in Figure 3, both tasks exhibit consistent decline in Mi-FI as increases. This suggests that stronger alignment (i.e., larger 7)) may induce excessive regularization, hindering the model's s ability to preserve task- specific discriminative features. Additional results are provided in Appendix E.4.
Study on Diffusion Step As shown in Figure 3, the Mi-Fl score for - improves with increasing T and stabilizes beyond T 40, suggesting that sufficient number of diffusion steps necessary to effectively capture structural dependencies. A similar trend is observed U + E, where performance peaks at T 80 and fluctuates slightly thereafter. These results indicate that while adequate diffusion depth important, excessively large T yields diminishing returns. Additional results across datasets are provided in Appendix E.4.
5.5 MODEL EFFICIENCY ANALYSIS (RQ4)
Table 3 compares the runtime performance of four approaches: UDAGCN, DANE, GraphAlign and DiffGDA on two tasks, A D and A C, with all models trained for 150 epochs. Addition-

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70
80
Model
UDAGON
Sienerating Triining Total Mi-FI Genenting Training
83.19
83.19
67.52
104.9
Mi-FI
72.64
Micro-F1
80 -0
60
Dura
60
50
Ours
134.22
13492
DAME
DANE
GraphAllign
250.13
19.52
20065
70.1
27486
22.29
297.55 76.52
GraphAlign
30
GraphAigh
DiRCIDA
103.98
22.75
126.3
7341
10231
23.10
12541 50.23
100
150
100
150
Epachs
Epochs
Table 3: Runtime (seconds) and Mi-FI (%) comparison on two transfer tasks. All models are trained using single RTX 4090 GPU.
Figure 5: The training curves Mi-FI scores three baselines across two cross-domain transfer scenarios over 150 epochs.
(a) A2GNN
(b) UDAGCN
(c) GAA
(d) Ours
Figure 6: Visualization of node embeddings inferred by four models for the A - C task.
ally, the training progress visualized in Figure 5. While our method does not have the lowest absolute runtime, it achieves relatively lower total runtime compared to GraphAlign, a state-of- the-art approach for GDA based on graph generation, which exhibits significant time overhead due to intermediate graph generation. As shown in Table 3, our method effectively strikes a balance between graph generation
training time, reducing the total runtime by over 50% compared to GiaphAlign, with smaller training time and manageable graph generation cost. At the same time, achieves superior Mi-Fl scores on both tasks. Furthermore, Figure highlights that our approach not only converges faster but also consistently outperforms the baselines in terms of Mi-Fl scores across epochs. These results collectively demonstrate that our diffusion- based method offers a com- pelling trade-off between computational efficiency and performance, making it suitable choice for cross-domain tasks that demand rigorous experimentation and reliable outcomes.
5.6 VISUALIZATION FOR REPRESENTATION SPACE (RQ5)
To qualitatively assess the learned node representations, we visualize their distributions using SNE (Maaten & Hinton, 2008; Yuan et al., 2025), shown in Figure 6. In the plot, each color represents distinet class, enabling an intuitive evaluation of the clustering quality. Our method, DifiGDA, produces more compact and well-separated clusters compared to other models, especially the strong data-driven baseline, GAA. This improved clustering suggests a more effective separation of the underlying class distributions within the target domain. These results demonstrate that diffusion-basee adaptation process effectively mitigates ioraintirrelevant noise, enhancing inter- class discriminability and leading cleaner, more structured representation of the target graph.
CONCLUSION
In this work, we revisit the problem of Graph Domain Adaptation (GDA) from continuous genera- tive perspective. By framing cross-domain adaptation as stochastic diffusion process, our proposed method, DifIGDA, effectively models the joint evolution of structure and semantics in continuous time. This continuous formulation naturally captures smooth structural transitions and avoids the rigid assumptions of discrete alignment frameworks. The incorporation of guidance network ables the model to automatically learn the optimal adaptation path. Extensive empirical results across 14 transfer tasks validate the effectiveness and superiority of our approach.
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ACKNOWLEDGEMENT
This work was supported by the National Key Research and Development Program of China under Grant Nos. 2024YFF0729003, the National Natural Science Foundation of China under Grant Nos. 62176014, 62276015, 62206266, the Fundamental Research Funds for the Central Universities.
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Appendix
Table of Contents
Theoretical Proof
A.1 Proof of Theorem
15
A.2 Proof of Guidance Network Q
16
B Implementation details
17
Theoretical Analysis of DiffGDA's Error Bound
17
C.I Eror Bound Expression
17
C.2 Analysis and Insights
17
C.3 Practical Implications
18
Experiment Setup
D.1 Dataset Description
18
D.2 Baselines
18
D.3
Implementation Details
19
E. Experiment Results
20
E.1 Main Experiment Results
20
E.2
Significance test (t-test) of DifiGDA
20
E.3 Ablation Study
20
E.4
Hyper-parameter Analysis
21
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A THEORETICAL PROOF
A.1 PROOF OF THEOREM 1
Let Go and GO denote the source graph and target graph, respectively. Assume that the data distributions p and define the forward diffusion processes on the source and target domains, re- spectively. For consistency of modeling, we consider the forward process in the target domain to
share the same functional form as that in the source domain, i.e., p(G G ===gl q(G] [G Under this formulation, the optimal diffusion network P(e*) for the target graph GT satisfies:
q (G))
P((*)= Va log p: + Va log LogEppce p G
(16)
p (G))
where the first term is score function of the source graph, and the second term represents the gradient of the density ratio between the target and source graph distributions. The density ratio is defined as the likelihood ratio between the target and source domains in latent space. It reflects how domain- specific given representation is, and provides a directional signal to guide diffusion process.
Remark on Consistent Diffusion. In this theorem, we assume that clean graph data are corrupted in the same way in the source and target domains. Although the data distributions in the two domains (p(G)) and ((T)) )) are different, we assume they follow the same physical diffusion model (c.g., the same variance-exploding (VE) SDE). This common simplifying assumption that allows us to embed both domains into the same diffusion latent space for operations and comparisons. Based on these shared diffusion dynamics, inter-domain differences are entirely reflected in the differences of their initial-state (t 0) data distributions, and the core task of our guidance network Q is to estimate and compensate for this discrepancy via the density ratio (G ())
Proof: For clarity in the proof, we denote the left-hand side and right-hand side of Eq. (16) as LE and RE, respectively. Our goal is to prove the equivalence by transforming RE into LE, In the first step, establish connection between score matching the target graph and importance- weighted denoising score matching on the source graph. Drawing inspiration from (Vincent, 2011; Ouyang al., 2024), this relationship can be formalized
L' arg min E,
(
[|
Vor log q: (G.))
(17)
arg min E, ( [|P(C)) - Va log log G
((G)
p p(G))
The first term corresponds to score matching on source graph, while the second term incorporates importance weighting, bridging the connection to denoising score matching on the source graph.
g(CTT This adjustment is modulated by ) which accounts for the distributional differences between the source and target graphs, thereby ensuring consistent and unbiased score estimation.
Leveraging sepporaance-eiighed denoising score matching on the source graph, the optimal score can be formulated as:
P(()) En of)
Vas log pl GG LE. P(G))
(18)
EpGg
The final optimal solution IP((") is computed by normalizing the weighted gradient of the source graph's 's log-probability. The numerator captures the weighted score evaluation, while the denom- inator ensures proper scaling by accounting for the overall importance weights. This formulation guarantees an unbiased and consistent estimation, as the importance weights for any domain-level discrepancies.
correct
In the second step, without loss of generality, we consider an arbitrary graph G within the framework of the diffusion process p and proceed with the following derivation:
Ve, log p G. G.) VG, log GG) VG, log), This expression establishes the relationship between the conditional score VG, log G G.) and the components of the forward diffusion process, specifically the reverse transition probability and the marginal distribution at time
(19)
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Finally, based on Eq. (19), rewrite Eq. (16) as:
q (G))
RE = aa po G + aa log E ((Gf)))))
E GG
G G
G log p G -
Vas log pe
GG P(G))
E GG
[
V
GP log G G
(20)
a. log Pr p +
G
c log pr (G
(
[(
E PpG G
g G
as log pG )
LE
G )
EE B
Therefore, we have proven that Theorem holds.
A.2 PROOF OF GUIDANCE NETWORK Q
In this section, we demonstrate that Eq. (13) holds, namely:
((G)) = (()))) = log E (ogiof) p ((G))
(21)
where Q(Ō) denotes learned representation parameterized by d, and the logarithm is applied element-wise. To proceed, let us define p( p(G;) = pXX, A and (G,)) = q(X) AA) as the source and target joint distributions over node features X and adjacency matrices A, respectively. Note that, for simplicity of representation, we use as a shorthand for (X, A) throughout this proof. Thus, we have:
[G
8* arg min
Q(6)
p
(PG))
G
(G))
arg min
Ja
2(6)
GGGG.
(G
dG
pG: dG;
2
) ) +o
[G
arg min
[[Q(8)112 - 2 Q(0),
G
G
G
(GT) 2
arg min
2(6)
GGG G GG:
dG cG
MG
(G
arg min
Q(6)
(G G
dG
G(
(G p(
arg min E (
Q())
G
(22)
where C a constant independent of 8. According to Eq. (12):
(G)
8 (5, 55)
arg min Bn G8)
1(6)
(23)
pl G
5
Thereby we complete the proof.
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B IMPLEMENTATION DETAILS
Algorithm Density Ratio Estimation
Require: Source graph distribution p(G target graph distribution g(G)), ) pre-trained domain
classifier Conn. number of Monte Carlo samples Sme
Ensure: Estimated density ratio: P1
Sme
1: Train the domain classifier Cynn to distinguish G and G
2: Initialize accumulator: 71
3: for = 1 to Smc do
4: Sample G (i) p( (
5: Sample G (() g( (G))
6: Compute (0) Cynn ((1))
T(t)
Go
D For each node in the graphs
7: Calculate ratio: (+) 1-y(t)
y()
8: Accumulate: 1i + (()
9: end for
10:
return 5in
C THEORETICAL ANALYSIS OF DIFFGDA'S ERROR BOUND
In this section, we analyze the theoretical error bound of DiftGDA framework, focusing on the fac- tors that influence its performance under GDAsettings. By extending the traditional error bound framework and incorporating components specific to diffusion- basedd methods, we derive an expres- sion that characterizes the generalization error on the target domain as a function of multiple factors, including source domain performance, domain discrepancy, sample complexity, and noise stability.
C.1 ERROR BOUND EXPRESSION
Inspired by (Huang et al., 2024), the generalization error on target domain &y can be bounded as:
C
& S Es & D(Ps, PT)
+ + Raiff
(24)
VN
where Ey is the generalization error on the target domaín, Eg is the empirical error on the source domain, and D(Ps, Pr) represents the distributional discrepancy between the source and target domains, which can be measured using metrics such as MMD or Wasserstein distance. The term weight factor that scales the impact of domain discrepancy, influenced by the model's capacity and alignment mechanism. The term VN reflects a sample complexity term, where N represents the number of source domain samples, and C' denotes model complexity (e.g., Lipschitz constant or parameter count). Finally, Rail captures the residual error introduced by the diffusion process, which can be further decomposed into three controllable sources:
Raiff = f4 Bached(aming Fmax) + (lg Baise + f33 Eration
(25)
where 7), 12, 7/3 are non-negative coefficients weighting each term; Bached (amin: maxx) denotes the error from the variance-exploding (VE) noise schedule, controlled by the minimum and maximum noise levels min and 0max. Baise (T) is the discretization eтror of the reverse diffusion process, which decreases as the number reverse steps T increases. And Eratio the approximation error of the density-ratio guidance network, capturing the gap between estimated and true density ratios.
C.2 ANALYSIS AND INSIGHTS
The above error bound provides a comprehensive understanding of the factors that contribute to the generalization ability of DifiGDA in the target domain:
1. Source Domain Error Es: This error serves as the foundation of the target domain performance. A lower Es indicates that the diffusion model effectively captures the structural and semantic in- formation the source domain, which can be transferred to the target domain. If Eg is large, becomes challenging bridge the domain gap, even with dell-designed alignment strategy.
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2. Domain Discrepancy D(Ps, Pr): This term reflects the divergence between the source and target distributions. By leveraging the Nomain-aware guidance network in DifIGDA, the model min- imizes ((Ps, Pr) through adaptive alignment in the latent space. The density ratio term log p(G plays a pivotal role in reducing this discrepancy, ensuring that the generated graphs align closely with the target distribution.
(GG]
3. Sample Complexity VN: This term highlights the importance of having sufficient labeled sam- ples in the source domain. As N increases, the error bound tightens, indicating better generalization. However, larger models (with higher C*) may require more samples to avoid overfitting. DifiGDA mitigates this by efficiently generating intermediate graphs that maximize the utility of source data.
Diffusion Residual Rditt: The residual of the diffusion process is governed by three sources: (i) the noise schedule B.ched minn max)). which controls the stability of forward corruption and reverse denoising; (ii) the discretization error Baise (T), which decreases as more reverse steps are used; and (iii) the density-ratio approximation error Eatioo which depends on the accuracy of the guidance network. Each of these terms provides direct knob for improving error control.
C.3 PRACTICAL IMPLICATIONS
The error bound highlights three key aspects that influence the success of DifIGDA:
Reducing D(Ps, PT) through adaptive guidance and density ratio estima- tion is critical for effective knowledge transfer.
Domain Alignment:
Sample Efficiency: The ability to leverage limited source domain samples vital, especially in low-resource scenarios.
Diffusion Stability: Properly tuning the noise schedule, the number of reverse steps, and the accuracy density-ratio guidance jointly ensures robustness and lowers the residual error in GDA.
In summary, this error bound clarifies that the diffusion residual is not monolithic term but de- composes into three controllable sources, directly linked to design choices in DiftGDA. Optimizing these factors further improves the theoretical and practical guarantees of cross-domain performance.
D EXPERIMENT SETUP
D.1 DATASET DESCRIPTION
We perform node classification experiments under three migration settings in Table 2. In each sce- nario, we train our model on one graph and evaluate it on other graphs.
ACMv9 (A), Citationv1 (C), DBLPv7 (D): These datasets citation networks from different sources, where each node represents a research paper, and each edge represents citation relation- ship between two papers. The task is to predict the category of each research paper. The data are collected from ACM (before 2008), DBLP (2004-2008), and Microsoft Academic Graph (after 2010). We set six transfer scenarios: A C D. - A, C
D. - A, and D
USA (U), Brazil (B), Europe (E): These datasets are collected from transportation statistics and primarily contain aviation activity data, where each node represents an airport, and each edge represents flight connection between two airports. The task is predict the category of each airport. We set six transfer scenarios: U B, E, U, B E, E U, and E B.
Blogl (B1), Blog2 (B2): These datasets are taken from the BlogCatalog dataset, where nodes represent bloggers, and edges represent the friendship relationships between bloggers. The node attributes consist of keywords extracted from the bloggers' oef--desrrptioos. The task predict the corresponding group to which they belong. We set two scenarios: B1 B2 and B2 - B1.
D.2 BASELINES
We compare method with the following baseline methods, which can be divided into two cate- gories: (1) Graph Neural Networks (GNNs) on the source graph only: GAT (Veličković et al., 2018), GIN (Xu et al., 2019), and GCN (Kipf & Welling, 2017) trained end-to-end on the source graph,
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allowing direct application to the target graph; (2) Graph Domain Adaptation Methods: DANE (Zhang et al., 2019), UDAGCN (Wu et al., 2020), AdaGCN (Dai et al., 2022), StruRW (Liu et al., 2023a), GRADE (Wu et al., 2023), PairAlign (Liu et al., 2024b), GraphAlign (Huang et al., 2024), A2GNN (Liu et al., 2024a), GGDA (Lei et al., 2025), TDSS (Chen et al., 2025a), DGSDA (Yang al., 2025) and GAA (Fang al., 2025a) specifically designed address the GDA problem.
Below, we provide descriptions of the baselines used the experiments.
GAT, GIN, GCN, train using GAT, GIN and GCN under standard ERM.
DANE uses shared weight GCNs to get node representations and then handles distribution shift via least square generative adversarial network.
UDAGCN is model-centric method that first combines adversarial learning with GNN model. AdaGCN is a model-centric method for GDA. utilizes the techniques of adversarial domain adaptation with graph convolution, and employs the empirical Wasserstein distance between the source and target distributions of node representation as the regularization.
STRURW modifies graph data by adjusting edge weights, while the modification relies the training of data-centric GDA methods.
GRADE introduces graph subtree discrepancy metric measure the graph distribution shift by connecting GNNs with WL subtree kernel.
PairAlign not only recalibrates the influence between neighboring nodes using edge weights to address conditional structure shifts but also adjusts the classification loss with label weights to account for label shifts.
GraphAlign generates small, transferable graph from the source graph, which is used for GNN training with Empirical Risk Minimization (ERM).
A2GNN proposes simple GNN which stacks propagation layers target graph.
GGDA using the Fused Gromov- Wasserstenn (FGW) metric and adaptive vertex selection, ensures effective knowledge transfer between source and target domains.
TDSS applies structural smoothing directly to the target graph to reduce local variations and en- hance model robustness against distribution shifts. TDSS improves knowledge transfer by pre- serving node representation consistency while mitigating the impact of structural discrepancies.
DGSDA addresses GDA by disentangling node attribute and graph topology alignment. em- ploys Bernstein polynomial approximation for efficient spectral filter alignment, avoiding costly eigenvalue decomposition, and enables flexible GNNs for improved cross-domain adaptability.
GAA tackles both graph topology and node attribute shifts using attention- based cross-channel module for effective alignment, enhancing the model's focus on critical features.
D.3 IMPLEMENTATION DETAILS
We evaluate the model performance using Mi-Fl and Ma-F1 scores. The hidden layer dimension set to 64, and the learning rate is fine-tuned within the set {0.0001, 0.001, 0.01) to achieve optimal performance. Domain alignment is implemented using the MMD method with a Gaussian kernel (Keerthi & Lin, 2003). To prevent overfitting, a dropout rate of 0.2 applied. We adjust the parameters a within the range [0, 1]. within the range [0, 0.5), and T within the range [0, 150]. NVIDIA RTX 4090 GPU, running for 5 rounds
All experiments are conducted using PyTorch with 150 epochs per round. For each round, the maximum Mi-Fl and Ma-Fl scores are recorded, and their mean and variance are calculated.
In our diffusion models, we adopt the Variance Exploding (VE) SDE, defined by the following stochastic differential equation:
Umax
Tmax
dx = Jmin
V
2 log
dw.
(26)
Tmin
T
where Omin = 0.001, Omax = 0.01, and E (0, 1]. The transition probability density function
Pt.c-Se (FF (I:) Gaussian distribution with mean v, and covariance Σ,:
Pt, (2 604-8t xxe) = (x Ex),
(27)
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Blogi (B1), Blog2 (B2)
Methods
H2
#2 -3
BI
Avg.
Ma-FI
Mi-FI
Ma-F1
GAT (ICUR(18)
21. n5
11
19 45g
g5.30
GIN (CCLR19)
20.51
11.44
18 40..s
a.57
15.03 2..3
GCN (CCLR117)
23.17 17
13.8
23 45
g8.76
18.00, g.00..00
DANB (9CAF19)
28. 15
25.20.2.1s
25.37
28. 01 21.7
(WWW"22)
33.87
28.80 16
86g1 on
28.96 s0
AdoGCN (TKDE'22)
75
20.00 u
18.70a2m
24. 20.30
StrRRW (ICML'23)
10.37 s0.4
39.02.c.m
42.01
10.3
g0.84.n..0
GRADE (AAAT23)
48 18.44
44.46_4.
16.78
42.00
45. 12.42222.0
PaizAlign (ICML224)
10.01 p0
59.57
42.6420.8
41.96
g1.05
GraphAliga (KDD)22)
15.58
43.14
43.21
42 42.29
43. 13.00
AIGNN (AAAI224)
17. 10
45.12-4.7
44.01a20:
48.1
44.92
GGDA
20
45.09_...0
44.85aa
40.40g4
45.41g344
(AAAF25)
21.20
1illa1
10.50
DOSDA (1CML22)
48.01.1m
44.12
42.06
g..70
GAA (5))
18 45
45.66
43 74g1
40 m0.00
44.70.1.09
DIRGDA (Ours)
13.52
51.18
48.95
47.17
50.20.1.91
Table 4: Node classification performance (% + a) on the Social domains. The highest scores are highlighted in bold, while the second-highest scores underlined.
Dataset
A-*C
A
A->
Baseline - log, (0.05)
4.32
4.32
4.32
DifiGDA vs TDSS (AAAI'25)
16.29
13.57
7.43
DiffGDA AdaGCN (TKDE'22)
30.84
26.46
19.57
DiffGDA vs A2GNN (AAAI'24)
31.98
18.96
23.67
DifIGDA vs GraphAlign (KDD'24)
45.39
43.36
40.63
Table 5: Significance test (t-test) of DiffGDA
where E, is given by:
2t
26-2át
Σg = 2
O
mmux
(28)
min
m
After generating samples by simulating the reverse diffusion process, we quantize the elements of
the adjacency matrix to {0, 1} by clipping values the ranges (-o0, 3) to and [3, +cx) to 1.
The guidance network is a 3-layer MLP with 512 hidden units and ReLU activation functions. We train the guidance network for 100 epochs.
E EXPERIMENT RESULTS
E.
MAIN EXPERIMENT RESULTS
The experimental results on Blog domains are presented in Table 4.
E.2 SIGNIFICANCE TEST (T-TEST) OF DIFFGDA
To ensure that our method achieves statistically significant improvements, we conducted paired t-tests to compare the performance of DiffGDA against various baseline models across multiple transfer tasks, as presented Table 5. This rigorous statistical analysis was carried out at the 0.05 significance level, allowing us to objectively assess the superiority of our approach. We leveraged - llgg (p) values to quantify statistical evidence, where higher - log2(p) values indicate stronger support for the observed differences. By employing this approach, we aim to demonstrate its con- sistent and reliable performance across diverse tasks.
E.3 ABLATION STUDY
The more ablation results are presented in Figure
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Moso! 35
80
84
80
50
Mou EL
71
Figure 7: Classification Mi-FI comparisons between DifIGDA variants on other cross-domain tasks.
E.4
HYPER-PARAMETER ANALYSIS
The more pppem-paraeete results are presented in Figure 8 and Figure 9.
60
Micro-F1 (5%
Micros F1 (%)
70
Micro-FF (%)
B1-BB B2
55
B2
70
60
50
Micro-F1
45
80
80
35
0.1
0.2
0.3
0.4
0.5
0.1
0.2
0.3
0.4
0.5
0.1
0.2
0.3
0.4
0.5
0.1
0.2
0.3
0.4
0.5
0
Figure 8: The performances of our DifIGDA w.r.t varying weight 7) on different transfer tasks
A+
53
MitooF1 (5
Micro F1 (%5
Mirr F1 (%0
73
51
Micro-F1
46
49
41
20
40
60
100
20
40
60
100
40
60
80
100
80
100
Figure 9; The performances of our DiffGDA w.r.t varying step T on different transfer tasks
21


Reviews:
[{"review_id": "h3otdzoNzP", "reviewer": "Reviewer_h5bX", "summary": "This paper proposes DiffGDA, a diffusion-based Graph Domain Adaptation (GDA) method that models domain adaptation as a continuous-time generative process via Stochastic Differential Equations (SDEs). It integrates a domain-aware guidance network to steer the diffusion trajectory toward the target domain, jointly capturing structural and semantic transitions. Theoretical analysis proves the diffusion process converges to the optimal adaptation solution, and experiments on 14 transfer tasks across 8 datasets demonstrate consistent superiority over SOTA baselines. The paper’s formulation is rigorous, with clear definitions and solid mathematical proofs, and the implementation details are sufficiently detailed.", "questions": "I hope the author can provide in-depth responses to the weaknesses and questions raised.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "Graph Domain Adaptation (GDA) is a very interesting and meaningful research direction. The writing of this article is clear. The author has given proof of relevant theories and conducted a relatively comprehensive experimental design. DiffGDA’s advanced effects are worth checking out.", "weaknesses": "1. Applying the diffusion model (Diff) to the Graph scene is interesting,the author did not discuss in depth the advancement and challenges of symmetric diffusion processes, as well as the key differences with the advanced methods of Diff applied in Graph scenarios; at the same time, the difference between the diffusion model in the image/video generation field and GDA has not been deeply discussed, which makes me doubt the innovation and contribution of this paper.\n2. Lack of cross-domain (inter-domain) experiments: Current experiments focus on intra-domain transfers (e.g., citation → citation, airport → airport), where the data distribution has a similar pattern. Cross-domain transfer (e.g., citation → airport, social → citation) is more challenging and better reflects generalization, but it was not included, limiting the validation of the method's robustness to large distribution changes.\n3. Incomplete hyperparameter analysis of diffusion steps: The number of diffusion steps is a very important parameter. In image generation, the number of diffusion steps often exceeds 3,000, but the paper only tested up to 100 steps (is the node representation in the graph less difficult to learn than the pixel representation in the image?).\n4. The results do not clearly indicate whether the model has converged, and the impact of larger diffusion step sizes (e.g., 500, 1000) on performance and efficiency has not been explored. (If the author's GPU supports it)\n5. The necessity of using MLP is not explored: in image diffusion, UNet has been shown to effectively capture spatial dependence. The paper uses MLP for scoring and guiding networks, but does not discuss why MLP is superior or necessary for graph data, nor does it compare it to graph-specific architectures such as GNN-based scoring networks.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "oFd5t3ASpC", "reviewer": "Reviewer_wnSz", "summary": "This paper studies the problem of graph domain adaptation, where a model trained on a labeled source graph is expected to perform well on an unlabeled target graph with different structures and semantics. The authors propose a new method called DiffGDA, which views the adaptation process as a continuous-time generative evolution rather than a step-by-step alignment.\nThe method uses stochastic differential equations (SDEs) to model how graphs evolve from the source domain to the target domain, capturing both structural and semantic changes. A domain-aware guidance network is introduced to guide the reverse diffusion process toward the target distribution. DiffGDA is trained jointly with a graph neural network (GNN) classifier, and additional MMD alignment and adjacency constraints are used to maintain consistency across domains.\nExperiments on 14 cross-domain tasks from citation, airport, and social network datasets show that DiffGDA achieves higher accuracy and better efficiency compared with existing state-of-the-art methods.", "questions": "1. How does modeling the continuous generative process via SDE differ from standard DDPM-based diffusion approaches in terms of performance, efficiency, and stability?\n2. Could the proposed method be extended to handle heterogeneous or large-scale graphs?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. It formulates GDA as a continuous-time generative process via SDEs, unifying structural and semantic evolution.\n2. It provides a theoretical proof that the process works, which gives the method a solid foundation.\n3. It demonstrates consistent superiority over state-of-the-art baselines on 14 graph transfer tasks across 8 real-world datasets.", "weaknesses": "1. It models domain transfer as a continuous graph evolution process but lacks explicit interpretability or concrete tracking of graph structural changes.\n\n2. Diffusion-based methods are generally computationally expensive, and the scalability of the proposed approach to large-scale attributed graphs (e.g., ogbn-Products) remains questionable.\n\n3. Experiments are conducted only on homogeneous graphs, lacking evaluations on more realistic heterogeneous graphs (e.g., IMDB) to demonstrate broader applicability.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "1FmQgvhkZQ", "reviewer": "Reviewer_eQUv", "summary": "This paper introduces DiffGDA, a novel approach for Graph Domain Adaptation (GDA) that frames the problem as a continuous-time generative process. Instead of relying on discrete alignment steps or the construction of intermediate graphs, DiffGDA models the evolution from the source to the target domain using stochastic differential equations (SDEs), i.e., a diffusion model. The core contributions include: (1) A formulation of GDA as a continuous-time process that jointly models structural and semantic (feature) transitions. (2) A \"domain-aware guidance network\" designed to steer the reverse diffusion process, effectively learning an adaptation path from the source to the target distribution. (3) A theoretical justification (Theorem 1) showing that this guidance mechanism, by learning the density ratio between domains, converges to an optimal adaptation trajectory. (4) Extensive experiments on 14 transfer tasks, demonstrating that DiffGDA consistently outperforms state-of-the-art GDA baselines.", "questions": "See weaknesses.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. The core idea of modeling GDA as a continuous, time-driven generative process is novel and compelling. It directly addresses a clear limitation of existing data-oriented methods, which often assume a discrete or linear transformation between domains. The argument that real-world graph evolution is continuous and nonlinear provides strong motivation for this diffusion-based approach.\n\n2. The method is thoroughly evaluated against a wide array of recent GDA baselines (both model-oriented and data-oriented) across 8 datasets and 14 transfer tasks. The results in Tables 1 and 4 show that DiffGDA achieves state-of-the-art performance, often by a significant margin.\n\n3. The paper provides a solid theoretical foundation for its proposed guidance mechanism. Theorem 1 connects the optimal reverse SDE for the target domain to the source domain's score function plus a guidance term based on the density ratio $q(G_0^{\\mathcal{T}})/p(G_0^{\\mathcal{S}})$. This provides a principled basis for the guidance network's objective.", "weaknesses": "1. The primary concern is the practical efficiency and scalability of the proposed method. The framework involves training multiple components: a score network $\\mathbb{P}(l)$, a guidance network $\\mathbb{Q}(\\delta)$ (which itself relies on a pre-trained domain classifier $\\mathcal{C}_{gnn}$ for density ratio estimation), and a final GNN classifier. This represents a significant increase in complexity over simpler GDA methods. The \"Discussion on Computational Cost\" remark and the complexity analysis $\\mathcal{O}(T\\cdot n^{2} + L\\cdot(|\\mathcal{V}^{\\mathcal{S}}|+|\\mathcal{E}^{S}|))$ reveal a quadratic dependency on the number of sampled nodes $n$. This scalability issue is confirmed in the hyperparameter analysis for $\\alpha$ (Figure 3), where the authors report running \"out-of-memory\" on tasks $D\\rightarrow A$ and $D\\rightarrow C$ for sampling ratios above 50%. This practical limitation seems to contradict the claim that the method is efficient and suitable for \"modest computational resources.\"\n\n2. The implementation of the guidance network depends on estimating the density ratio $q/p$ by training a GNN classifier $\\mathcal{C}_{gnn}$ and using the approximation $(1-y)/y$. The stability and accuracy of this estimation, especially in the high-dimensional, sparse space of graphs, is a potential weak point that is not fully explored. The paper could be more explicit about the generation process. It appears the model generates a \"labeled graph\" $G'=(X', A', Y')$ by diffusing and reversing the concatenated input $\\tilde{X}^{\\mathcal{S}}=[X^{\\mathcal{S}}||Y^{\\mathcal{S}}]$. This is a key detail and implies that the model is learning to generate node labels as part of the diffusion process, which is an interesting but non-trivial aspect of the design.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)