Diffusion-Guided Graph Data Augmentation
Authors: Maria Marrium
Arif Mahmood
Muhammad Haris Khan
M. Saad Shakeel
Wenxiong Kang
Venue: NeurIPS 2025 poster ()
Keywords: diffusion based graph data augmentation
node classification
link prediction
graph classification
Primary area: other
TL;DR: A generalized diffusion based graph data augmentation method.

Abstract: Graph Neural Networks (GNNs) have achieved remarkable success in a wide range of applications. However, when trained on limited or low-diversity datasets, GNNs are prone to overfitting and memorization, which impacts their generalization. To address this, graph data augmentation (GDA) has become a crucial task to enhance the performance and generalization of GNNs. 
Traditional GDA methods employ simple transformations that result in limited performance gains. Although recent diffusion-based augmentation methods offer improved results, they are sparse, task-specific, and constrained by class labels. In this work, we propose a more general and effective diffusion-based GDA framework that is task-agnostic and label-free.
For better training stability and reduced computational cost, we employ a graph variational auto-encoder (GVAE) to learn a compact latent graph representation. A diffusion model is used in the learned latent space to generate both consistent and diverse augmentations. 
For a fixed augmentation budget, our algorithm selects a subset of samples that would benefit the most from the augmentation.
To further improve performance, we also perform test-time augmentation, leveraged by the label-free nature of our method.
Thanks to the efficient utilization of GVAE and latent diffusion, our algorithm significantly enhances machine learning safety measures, including calibration, robustness to corruptions, and prediction consistency. Moreover, our method has shown improved robustness against four types of adversarial attacks and achieves better generalization performance. 
To demonstrate the effectiveness of the proposed method, we compare it with 30 existing methods on 12 benchmark datasets across node classification, link prediction, and graph classification in various learning settings, including semi-supervised, supervised, and long-tailed data distributions. 
The code will soon be made publicly available.

Diffusion-Guided Graph Data Augmentation
Maria Marrium', Arif Mahmood', Muhammad Saad Shakeel'
Muhmmad Haris Khan',
Wenxiong Kang²
Information Technology Univeristy, Lahore, Pakistan ²MBZUAI, Abu Dhabi, UAE
Soutth China University of Technology, Guangdong, China
(phdcs22002, arif mahmood) @ith eit.. muhammad www.haarrruuaai. ac (saadshakeel, auwxkang) @scut. edu. cn
Abstract
Graph Neural Networks (GNNs) have achieved remarkable success wide range of applications. However, when trained on limited or low-diversity datasets, GNNs are prone to overfitting and memorization, which impacts their generalization. To address this, graph data augmentation (GDA) has become crucial task to enhance the performance and generalization of GNNs. Traditional GDA methods employ simple transformations that result in limited performance gains. Although recent diffusion based augmentation methods offer improved results, they are sparse, task-specific, and constrained by class labels. In this work, propose more general and effective diffusion-based GDA framework that is task-agnostic and label-free. For better training stability and reduced computational cost, ploy graph variational auto-encoder (GVAE) to learn a compact latent graph representation. A diffusion model used the learned latent space generate both consistent and diverse augmentations. For a fixed augmentation budget, our algorithm selects a subset samples that would benefit the most from the augmen- tation. To further improve performance, we also perform test-time augmentation, leveraged by the label-free nature of our method. Thanks the efficient utiliza- tion of GVAE and latent diffusion, our algorithm significantly enhances machine learning safety measures, including calibration, robustness to corruptions, and prediction consistency. Moreover, our method has shown improved robustness against four types of adversarial attacks and achieves better generalization perfor- mance. To demonstrate the effectiveness of the proposed method, we compare it with 30 existing methods on 12 benchmark datasets across node classification, link prediction, and graph classification in various learning settings, including semi-supervised, supervised, and long-tailed data distributions. Code available at http://lthbbb.oo///Maaaaaaaaaaae
Introduction
Graph Neural Networks (GNNs) have achieved remarkable success across diverse domains, such as social networks 29 16 recommendation systems (7] and molecular property prediction 4 53
However, their expressive power makes them prone to overfitting and memorization, particularly when trained on limited, imbalanced, or low-diversity graph datasets [54] 90] 36 7 87]. These
limitations undermine their generalization diverse test scenarios, posing a significant challenge for real-world applications [92]. To address this challenge, Graph Data Augmentation (GDA) has emerged as promising strategy to enhance the generalization of GNNs by improving the diversity of training data [8 455 Traditional GDA methods are based on static transformations, such as node feature alterations
edge modifications
or subgraph manipulations 2 72
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

THETTA
10
Random Samples
TSS Accepted Samples
TSS Rejected Sumples
<bropldee <TLac
Caln Acc, (%0
Tan ad Cembooay
+0-GDA
PLAG
Desphalge
Pulmnd
Products
Flickr
Tob-act Dioentty
(h)
Figure I: a) Node classification performance comparison: baseline GCN (zero-line). augmenting 20% random, 20% TSS-rejected, and 20% TSS selected samples. (b) Diversity vs. consistency averaged over the same six datasets. Top-right corner shows a good balance of diversity vs. consistency.
However, these approaches often fail to balance consistency (preserving the original labels) and diversity (introducing meaningful variations), as illustrated in Figure Tb Recent diffusion- GDA methods, such as Data-Centric Transfer (DCT) 440 and Diffusion on Graph (DoG) [ leverage diffusion models to generate synthetic graphs or nodes, offering improved results. However, these methods are task-specific and rely on class labels that limit their applicability to general tasks. Moreover, GDA methods have not been thoroughly evaluated for robustness against adversarial attacks and machine learning (ML) safety measures, such as calibration, corruption, and prediction consistency (see Table !T.
To overcome these limitations, we propose Diffusion-basee Graph Data Augmentation (D-GDA), which novel, applicable different graph tasks and label-free framework. It improves the generalization of GNNs in various graph tasks, including node classification, link prediction, and graph classification. The D-GDA introduces three key concepts: (1) Target sample selection, which identifies candidates for effective augmentation to maximize performance gain. It helps D-GDA focus training data space (Figure Tab; (2) Gruph variational auto-encoder, to
on challenging regions encode local graph structure and semantics into compact latent space to reduce computational cost without affecting performance; (3) Latent Diffusion Model, which generates consistent and diverse synthetic nodes and edges conditioned on neighborhood embeddings. It ensures that the generated augmentations preserve local graph structure while introducing meaningful diversity (Figure [b). Unlike prior diffusion-based GDA methods, the proposed D-GDA is label-free, and therefore, it can be used to augment the test samples to improve performance. The test-time augmentation [27 has not been well studied in the graph data. We observe a consistent performance gain by performing test-time augmentation in graph and node classification tasks.
Table 1: comparison of SOTA GDA methods: 1) Basic building blocks: graph auto-encoder
(GAE), Graph Variational auto-encoder (GVAE), and Diffusion models. 2) Supported tasks: Node Classification (NC), Link Prediction (LP),, and Graph Classification (GC). Robustness evaluations:
adversarial robustness (Adv) and machine learning safety measures (MSM). 4) Learning Settings: semi-supervised, Supervised, and Long-tailed (LT). 5) Test- Time Augmentation (TTA).
Basic Building Blocks
Supported Tasks
Robustness
Learning Setting
Methods
TTA
GAE
GVAE
Dift.
NC
LF
GC
Adv
MSM
Semi
Sup.
LT
DropEdge 54
X
X
X
GAug 90
X
X
X
X
FLAG [1
X
X
X
X
X
LA 42
X
V
X
J
X
X
X
GraphPatcher [25
X
X
X
V
X
V
DCT 40
X
X
Y
V
X
X
LeDA [1
X
DoG 71
V
X
X
X
GraphVCM
52
X
X
X
X
D-GDA (ours)
x
V
V
V
2

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The proposed D-GDA offers several advantages over existing methods, including performance gains, improvements in ML safety measures, robustness adversarial attacks, and lower computational cost compared to other diffusion-based methods. MI. safety measures include calibration, corruption, and prediction consistency. D-GDA improves robustness to Random, DICE, GF, and Meta-Attacks. D-GDA is evaluated in semi-supervised, supervised, and long-tailed classification settings, demon- strating consistent improvements. D-GDA also achieves a good balance of diversity vs. consistency over existing compared methods. Through extensive experiments on 12 benchmark datasets for node classification, link prediction, and graph classification, D-GDA has shown excellent performance compared to 30 state-of-the of-the-art art methods.
Contributions: (1) We propose D-GDA, label-free. diffusion- graph data augmentation framework that excels in node classification, link prediction, and graph classification across semi- supervised, supervised, and long-tailed settings. It supports test-time augmentation for enhanced performance. (2) D-GDA leverages variational auto-encoder and latent diffusion model for proposed neighborhood- aware node generation.
(3) D-GDA introduces a Target Sample Selector to select effective candidates resulting in overall performance improvement for fixed augmentation budget. (4) D-GDA enhances ML safety measures including calibration, resistance to corruption, and consistency. It is more robust against adversarial attacks (Random, DICE, GF, Meta-Attack) and converges to flatter minima for improved generalization and reduced over-smoothing.
2 Related Work
Traditional Graph Data Augmentation methods do not rely on generative models. Instead, they apply augmentations by modifying the graph structure features-such as adding/removing edges
[Z [0]. altering node features [I 68 73). or manipulating subgraphs [48] 72, 14
65
82
Some
methods also adopt hybrid strategies that combine multiple techniques [80 64
83
32
76)
For
instance, DropEdge (54] randomly removes edges for regularization, and FLAG BII introduces
gradient-based feature perturbations. GAMS 2 partitions graphs into clusters, computes inter-cluster similarity, and swaps the most similar clusters. GeoMix [91 incorporates spatial structure through geometry-ave aware mixup. Notably, these methods modify existing graphs without increasing dataset size, whereas D-GDA explicitly enlarges the training set by generating new, task-relevant augmented samples. Generative Graph Data Augmentation methods leverage generative models to enrich graph data. LA 42 uses a Variational Graph Autoencoder (VGAE) to generate local node features for augmentation. DCT [40] focuses on graph classification, generating entire graphs conditioned on graph-level properties. DoG 77] targets node classification and employs diffusion model conditioned on class labels to synthesize node features. In addition to these, there are methods that generate molecular graphs conditioned
input graphs using both GVAE [8] 58) and diffusion models [2 69 38 5 9.. However, these approaches primarily focus on generating valid molecules, and their effectiveness for improving graph classification performance remains unexplored. In contrast, D-GDA is a versatile framework applicable to node classification, link prediction, and graph classification. Rather than conditioning on class labels, it introduces neighborhood-aware conditioning to guide the diffusion model denoising process, enabling context-aware and task-relevant augmentations that enhance performance across diverse graph tasks. Class Imbalance Handling methods tackle class imbalance in graph data by primarily augmenting minority class nodes to balance the training set. Recent approaches include GraphSMOTE [87. ImgAGN (51), GraphENS [49], GraphSHA (37), and Graph [52]. These methods typically use mixup to generate new node features and connect them either to the neighbors of both mixed nodes or just the target node. A comprehensive survey of such techniques is provided by [44] In contrast, D-GDA focuses on difficult-to-eaarn nodes and employs GVAE and LDM models to generate augmentations with selected nodes. Masked Autoencoders learn robust representations by masking parts of the input and training the model to reconstruct the missing content. Originally popularized in NLP with masked language modeling 12, this approach has been adapted for graphs via Masked Graph Modeling (MGM) 47 66), which predicts masked node features and edges. We leverage MGM into our GVAE framework to enhance the quality of latent representations for our latent diffusion model.
3

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1) TSS
TSS
G-ALX
Sumple Selector
(-(A,))
LDM
Z
F
B) Link Prediction
Porword Diffasion
D
G-AXX
GPA(ACC))
Bevens Diliiion
D2
LDM
GVAE
ii LDM
ii GVAE
G'AXX
A) Node Classification
Graph Classification
Target Node
Augmented Node
Target Edge
Augmentted Edge
Figure 2: Overall architecture of the proposed D-GDA framework: A) Node classification: i) We
propose Target Sample Selector (TSS) to select challenging-to--ean nodes. ii) harness Graph Variational Autoencoder (GVAE) to encode the graph structure into latent representation. GVAE decoders reconstruct augmented node features and edges from the latent space. iii) Latent Diffusion Model (LDM) generates neighborhood-awez
latent representation. B) Link Prediction: TSS selects challenging Larnggtt-llcre to-learn target links. GVAE encodes graph latent representation. LDM generates augmented node latent representation based on average aggregated edge neighborhood. C) Graph Classification: TSS selects challenging-to- to-lear target graphs. GVAE encodes each graph to latent space. Maximum degree nodes selected as target nodes. Augmented nodes are generated using LDM based on target node neighborhood.
3 Methodology
Preliminaries: Let G (V, E) be graph, where V = {1r } be the set of n nodes and & be that set of edges. Each node is associated with feature vector 2; Rd and X = [x I2,.... .., Fnl _ E Rad be the feature matrix. The edges are encoded adjacency matrix A Raxn, where A.j Wiy if there is an edge from v; to Uj. and 0 otherwise. Graph Neural Networks (GNNs) learn low-
dimensional node representations H E Raxd by aggregating neighborhood information. A common GNN variant, Graph Convolutional Network (GCN) [29] updates node embeddings layer-wise as:
( a (D- AD + HHO
where, À A + is the adjacency matrix with loofsloops, D is its corresponding degree matrix, H = X is the initial node feature matrix, W() E Rdixd++1 is the weight matrix layer 1, and a()) is a non-linear activation function such as ReL.U. The final layer output, H. provides node embeddings for downstream tasks. Node Classification: For graph G with Vi V labeled nodes with labels YN { where V; R is one-hot vector for classes. The H passed through softmax layer for classification. Link Prediction: For graph G. node embeddings H are used with a scoring function (e.g., inner product) to predict edge (link) likelihood between node pairs. Graph Classification: For a set of graphs G (GI.... Gm with labels YG. the node embeddings H are aggregated using a cottuutttioniivvriiain readout layer, for example, mean pooling, to obtain the graph representation TG,, followed by the classification layer.
3.1 Proposed Diffusion-based Graph Data Augmentation (D-GDA) Framework
Our proposed D-GDA framework enhances GNN generalization by generating diverse augmentations. D-GDA comprises of three components: (I) new Target Sample Selector (TSS) identify samples

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that maximize augmentation advantage, (2) a Graph Variational Autoencoder (GVAE) to learn compact latent representations to reduce computational complexity, and (3) a Latent Diffusion Model (LDM) to generate augmentations which we propose to be conditioned on target node neighborhood. The overall D-GDA framework is shown in Figure
3.1.1 Target Sample Selector (TSS)
Given fixed augmentation budget, our TSS selects subset of samples that would benefit the most from augmentation, thereby improving overall performance. In Figure Ta a comparison is shown for node classification using a budget of 20%. A comparison of Randomly-selecte and TSS- TSS-rejected samples demonstrates the importance of this stage. For this purpose, we train baseline GNN and compute the entropy (e,) of the predicted class probabilities for each sample s:
TSS-selected,
6, - - Ps logps" where c is the number of classes and ps is the prediction probability for i-th class. High entropy indicates prediction uncertainty, marking samples difficult to learn. The samples are sorted in descending order based on entropy ég. If the augmentation budget corresponds k-samples, the top-k samples are selected as augmentation targets from the sorted list. The bottom k samples of this list are considered as TSS- ISS-rejected samples.
(4) (c)
3.1.2 Graph Variational Autoencoder (GVAE)
In our proposed framework, the latent diffusion model (LDM) is used for the generation of augmented samples. Training of LDM is more stable and computationally efficient in latent representations (21). Variational graph autoencoders learn expressive latent representations of graph data, capturing both
node features and local structure [30 34 47). Therefore, we employ a variant of this architecture for compact latent representation learning, resulting in reduced computational complexity and improved performance. Our GVAE consists of a GCN-based encoder and two decoders for node feature and edge reconstruction. The GVAE consists of a GCN- based encoder and two decoders for node feature and edge reconstruction. GVAE Encoder maps node feature matrix X and the graph adjacency matrix A to a latent space representation by learning Gaussian distribution. It first applies 1,-1 layers of graph convolution to compute intermediate node representations H (See Eq. 11. Then, it is used to parameterize the mean and variance of a Gaussian distribution: log 2² fo (H A), where, f and fo denote separate GCN layers acting
f = ( (H--1, as linear transformations. To enable tradient-based learning through stochastic sampling, the latent embedding Z is drawn using the reparameterization trick (28] = - Se, e~ NO, I), where @ denotes element- wise multiplication. The resulting vector Z E Raxd, is the latent representation of G. GVAE Feature Decoder reconstructs the original node features x, from the latent variable 2, using a multilayer perceptron: x; (z. Feature decoder constraints the latent space to preserve semantic information about node attributes and serves as auxiliary supervision signal. GVAE Link Predictor reconstructs the graph structure by estimating the probability of link (edge) between node pairs (c;, U;) based on their latent representation: p.j (fiin (z, (2,)) where (.)) is the sigmoid function and || shows concatenation operation. Link predictor constraints the model to learn structural dependencies and reconstruct the adjacency matrix from the latent space Z. Regularization: To improve effectiveness of GVAE, we use two different regularization strategies, including edge masking [34] and feature masking 47). Edge masking randomly removes subset of edges during training, forcing the model to reconstruct them from partial graph. Feature masking randomly zeros out a fixed percentage of node features coefficient, encouraging generalization. GVAE Loss Function: The GVAE is optimized with an overall loss: LEVaE = Ledge + > Creat + A2L
where, Lient = Σ, l|x; x: is the feature reconstruction loss that measures the Euclidean distance between original and reconstructed node features, Ledge = ((t)) log -((.)) (- is the link prediction loss with sub-sampling of non-edges for balancing both type of samples, CKL DxL [ę(z,(x,) xx) (o, I)] is the KL divergence loss used to regularize the learned latent distributions (2, xx) to match a standard Gaussian prior, and \1 A are hyperparameters used as reported by [30].
3.1.3 Latent Difffusion Model (LDM)
The LDM generates diverse augmentations in the GVAE latent space by leveraging a Denoising Diffusion Probabilistic Model (DDPM) (11). This approach is more efficient than diffusion in the input graph space due to improved training stability and reduced augmentation overhead. In addition,
5

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it can effectively capture local structure through conditioning. In the forward (diffusion) process. Gaussian noise is gradually added clean latent vector z over sequence of T time steps. At each step E (1,..., T) the noisy latent vector Z4 is computed as: 2 var 2 + v 04 6, where, c <~ (O, a IT== ass where a, E (0, 1) are predefined noise schedule parameters controlling the rate at which noise is injected. This process transforms a structured latent vector into nearly pure Gaussian noise vector t T.
Reverse Process with Proposed Conditioning: The existing LDM reverse process aims to recover the clean latent representation z solely from a noisy latent vector 2f. Such reverse process may generate augmentations far from the target samples resulting in performance degradation. To handle this issue DoG [7]] constrained noise recovery process by class-labels. However, due to intra-class variations it does not ensure the generated augmentation to be close to the target sample. Also, the requirement of class-labels restricts the augmentation to training set only. In contrast, we propose the generation process to be constrained using target-node neighborhood which better encodes a difficult to learn regions. Being label-free, D-GDA is able to extend augmentations beyond training set for better utilization the graph structure, resulting in improved performance. Our proposed conditioning vector cf, encodes the local topology by mean aggregating the one-hop neighborhood embeddings 2) of node 0;: of = (e,((,,) 2z. A denoising network cg, implemented as a ID-UNet (55) predicts the noise c using 2f. and cº. formulated as é = co(z), t, c.). The LDM is trained with a denoising score matching loss: Lair Ex || 11 which ensures the predicted noise aligns with the true noise. By leveraging both temporal dynamics and our proposed neighborhood-awe awaae conditioning, our approach achieves superior denoising and generates structurally coherent augmentations.
3.1.4 Task-Specific Augmentation Generation
D-GDA adapts its augmentation strategy to each task, using TSS, GVAE, and LDM to generate augmented samples.
Node Classification: For each TSS-selected target node uy we encode its one-hop neighborhood N(v;) via the GVAE encoder to obtain the proposed conditioning vector cf using mean aggregation. The LDM generates a new latent vector (Aug.i) conditioned on cf which is then decoded into feature vector X (Aug.s) using feature decoder of GVAE. The augmented node is linked with the most probable neighbor of i as determined by the GVAE link predictor. The augmented node V(Aug. is given the same label as Ug, and is added to the training set. Such neighborhood-aww augmentation allows better learning of the structurally hard nodes in the graph, ultimately enhancing generalization and robustness.
Link Prediction: TSS selects a set of target links each defined by its adjacent nodes (1), 02). For both of these nodes, we encode their 1 h-hop neighborhood nodes using GVAE encoder. An aggregated conditioning vector cf = (cf c)) ) is computed by averaging across both neighborhoods. Using Cj an augmented node latent vector ((Augú.)) is estimated using LDM and decoded to feature (() and is connected to both nodes U; and By. Such an augmentation guides the link prediction model to focus on Shalleeginngto-leate links in given graph.
Given a set of graphs G, TSS is employed to select a subset of target graphs for augmentation. For each selected graph G,, the top-y highest degree nodes are identified as target nodes and for each of these nodes the augmentation procedure as discussed in the node classification section is followed. Selecting high-degree nodes ensures that the augmentation has a significant impact on the overall graph representation, as these nodes are more structurally influential. In contrast, augmenting low-degree nodes has minimal effect on the global structure, leading to less meaningful variation. Our augmented graph G (Aug.)) inherits the label of its corresponding target graph G; and is added to the training set, thereby enriching data diversity and enhancing model generalization.
Graph Classification:
Test- Time Augmentation: The test-time augmentation has not been well explored in GDA (25.. Our proposed D-GDA being label-free is able to perform augmentation in test sets in node and graph classification tasks. Such augmentation facilitates efficient usage of graph structure resulting in performance improvement, without label assignment. During inference, we set each test-sample as target and obtain its augmentation. The labels are predicted for both original and augmented samples. If different class labels are assigned, then the most confident label is selected as the final label.

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Table 2: Node Classification performance comparison of D-GDA framework with SOTA methods small-scale datasets. Best and 2nd best performances are in bold and underline, respectively.
Method
Cora
Flickr
Citeseer
Pubmed
Mean
GCN 29
0.76
61.20++0.0
71.60+0.40
78.80+0060
73.30
+roppEdee
8.800:10.80
6..40:10.70
7..00:0.20
07.30:0.32
73.13
AdaEdge
81.90:10.70
61.20:10.50
0.78
77.40:1.550
73.33
Node/Au
80
82. 1..900
7..40.0.60
78.80 1:040
77.43
GAuug (90)
83,60.10.50
62.20:10.30
73.30.1
80.2010.30
74,83
Graph Mixup
73.80.10.02
64.30.10.04
76.60.0.118
71.57
+FLAG 31
75.20.10.40
62.90.10.20
62.70100.0
78.50.10.01
69.83
+LA 55
84.60.10.50
64.2410..0
74.7010.50
81.70.0.70
76.31
+NASA R
85.10.1..30
75.50
80.2011..00
80,30
+DropMessage
13
83.33+0.11
53.55++023
71.83+0.09
79.20=00.06
71.98
+S-Mixup
26
84.78+00.15
14.39=0.10
79.70+0.117
79.62
+DropEdge++
83.10++0.12
63.18+00114
72.70+0.006
80.00+0.42
74.75
GGraphPatcher
25
84.17+0.544
71.65+0.05
81.13+0.688
78.98
+GrraphMxx
23
83.78+0042
53.61 +1.12
73.67+0.61
79.93+0.60
72.75
*SkipNode
43
82.00++0.40
50.73++0009
69.60+0.50
77.50+0.70
69.96
GeoMixx 91
84.08+0.74
75.06+0.36
80.06+0.93
79.73
+RGDA 39
84,33+00.41
73.02+0.36
82.08+0.50
79.81
+LcDA 41
78.60=00.32
62.64:10.32
67.50=00118
79.70=0.02
72.11
+DoG 71
84.00:1..30
73.60=0.40
82. 82.0003.30
80.13
+D.GDA (ours)
09.10::0.22
87.30 1.66
81.50 0.15
88,20 0.118
86.53
4 Experiments
Experiments for Node Classification Task: We evaluate D-GDA four small-scale datasets: Cora, Citeseer, Pubmed [56]. and Flickr [46] and two large-scale datasets: Ogbn- Arxiv [22], and Ogbn-Products [22] under transductive learning. Following [29]7] 7
we use semi-supervised settings for the small-scale catasstts and following [22 supervised settings are used for the large-scale ones. D-GDA outperforms both the baseline GCN and compared SOTA methods across all datasets as shown in Tables 2 and Compared to GCN, D-GDA improves test accuracy by 7.5% for Cora, 26.1% % for Flickr, 9.9% for Citeseer, 9,4% for Pubmed, 3.18% for Ogbn-Arxiv, and 7.48% for Ogbn- Products. We also evaluate D-GDA on GNN backbones including GAT (67] and GraphSAGE [16] as shown in Table 4 where D-GDA again surpasses existing methods. On Cora, Citeseer, and Pubmed, improvements with GAT are 4.7%, 4.3%, and 9.1 1.1,, and with GraphSAGE are 5.3%, 7.5%, and 7.4%, respectively. More comparisons shown in Appendix B.2 More details of all datasets are given in Appendix(B.]
We evaluate D-GDA on five link prediction benchmarks: ogbl-collab, ogbl-ddi, Cora, Citeseer, and Pubmed using GCN (2 and GSAGE [16] backbones and the results are shown in Table 5] D-GDA consistently outperforms existing methods on most datasets and backbones, with notable gains on smaller citation datasets. More results are shown in Appendix B.3
Experiments for Link Prediction Task:
Table 3: Node classification performance com- parison large-scale datasets.
Table 4: Node Classification Performance D- GDA on GAT 667 and GSAGE [66] backbones.
Method
Ogbn-Arxiv
Ogbn- ProduPs
Method
Cora
Citeseer
Pubmed
GCN 29
71.62+0..2
71.37=0.50
Vanilla
81.3
70.5
79.4
+dropEdge
56.26+t0.02
56.41=3.40
+GAug
82.2
71.6
79.3
+FL.G 31
71.75-10.01
76.14-1..30
GAT
+LA [42
84.7
74.7
79.8
+SkipNode
43
81.6
68.4
77.6
+LA 42
72.08-10.14
76.11
+D-GDA (ours)
89.4
79.0
88.9
Mesoaes 13
71.27+0.02
Vanilla
81.3
70.6
76.8
+RGDA [39
72.88:10.65
OSAGE
+GAug (%0
83.2
72.7
78.5
+DoG 71
+3.10
+SkipNode
81.5
68.5
77.4
+D-GDA (ours)
70.80
78.85 0.24
+RGDA
83.4
72.6
82.1
+D-GDA
88.7
80.2
89.5

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Table Link prediction performance comparison with SOTA methods.
Ogbl-collab
OgbI-ddi
Cora
Citeseer
Pubmed
Method
(Hitss@00
(llits@20))
(AUC)
(AUC)
(AUC)
Vanilla
44.75=1.00 1.07
37.07+5.07
89,55-10.53
69.47=1.40
96.11+0.00
+FLAG 31
46.22.1088
51.41
91.34.10.25
83.6310.73
96.2110.52
GCN
+CFLP 89
1..51
02.55=+0.50
89,65=0.20
96.99:t0.08
+GM (63
59.18+2.09
92.02=+0.45
90.61=0.30
97.35=+0.15
+D-GDA (ours)
50.24
57.53++0.15
96.96-10.15
93.72-10.36
97.82-+0.18
Vanilla
48. 0.81
53.9014.74
91.14:1..4
86,9811.39
16.78
GSAGE
+FLAG 31
48.44 0.40
63.31+6.06
91.52++042
90,48+0.19
96.89++0.14
+CFLP 89
4..49+4.33
92.61+0.552
91.84+0.20
97.01+00.01
+GM 633
7.12
92.41
92.85
98.62-10.09
+D-GDA (ours)
51.08-0.33
78.82+0035
97.62+0.35
95.64+0012
9..8
Table 6: Graph Classification Performance (ROC-AUC) comparison with SOTA methods.
Method
ogbg-molSIDER
ogbg-molClin
ogbg-molHIV
ogbg-molBACE
Vanilla [29]
59.60 1.17
88.55+22.09
76.06+00.97
71.4770.32
+FLAG [31
59.92-0.05
92.06+00.32
76.83+1.001
74.28+1.16
GCN
+RGDA 39
63.16-1.2. 1.51
1.56
77.94.10.65
81.9112.441
+D-GDA (ours)
0.32-0.32
94.82:10.12
79.03+0.92
83.45+0.85
Vanilla
58. 38.10=0.90
88.80+3.800
75.58+1.40
77.50++2.80
+FLAG [31
60.74-0.07
87.7510.16
7..5411.14
79.10:1
GIN
+G-Mixup [8
56.80=3.50
60.20+7.50
77.10+1.10
77.80+
+DCT 40
0.30
92.10:10.80
79.50+11000
85.60:40.60
+ +RGDA
39
60.14 2.04
87.89-13.68
79.32+00.22
82.37-42.37
+D-GDA (ours)
64.83 0.14
94.72.10.48
19.45=1.37
86.12:10.98
Experiments for Graph Classification Task: We evaluate D-GDA on four graph classification bench- marks: ogbg-molSIDER, ogbg-molClinTox,, agbg-molHIV, and ogbg-molBACE, using GCN (29) and GIN (79 backbones. D-GDA outperforms compared SOTA methods on most datasets and backbones as shown Table Additional details are given Appendix B.4
Experiments on Long Tailed Datasets: We evaluate D-GDA on two long-tailed datasets, Cora-LT and Citeseer-LT, with imbalance ratio of p 100 to assess its performance under class imbalance. Unlike prior methods that focus on oversampling minority classes, D-GDA adopts a class-agnoss strategy by identifying and selectively augmenting challenging samples. As shown in Table 7 D- GDA achieves consistent improvements on both datasets without requiring mabalance-specinf tuning. highlighting its effectiveness in long-tailed settings. Additional results provided in Appendix B.5
Improvements in ML Safety Measures. We evalu- ate D-GDA on three ML safety measures: calibration (assessing how well predicted probabilities reflect actual correctness), corruption (robustness to input perturbations), and consistency (stability of predic- tions under minor input changes). Models are trained on clean data and tested across these tasks. D-GDA shows strong performance on all metrics (see Table More details in Appendix B.6
Table 7: Balanced accuracy (%) comparison under class imbalance (p = 100).
Method
Cora-LT
Citeseer-LT
GCN (Vanilla)
59.42=0074
44.64=0.42
+ReNode g
67.61-1.133
47.7810.31
+GraphSMOTE
87
66.29-10.33
44.4010.29
+GraphENS 49
70.31+0.24
55.42-0.35
+TAM (G-ENS)
72.1010.233
57.15-10.4
+GraphSHA 37
74.62-1029
59,0410.41
+GraphVCM [52
75.81=0042
60.53+
+D-GDA (ours)
00.34-00.5
64.95
Adversarial Robustness. We evaluate D-GDA robustness aganntt four evasion attacks: Random
(randomly flip edges), DICE (74) (deletes intra-class edges and adds inter-class ones), GFAttack
[6] (optimizes a low-rank loss for structural perturbations), and Meta-attack [93] (meta-gradient- based loss maximization), at two perturbation ratios (a 0.05, 0.2). Table 9 shows improved node classification accuracy under these attacks compared to baseline GCN. More details are in Appendix B.7
we analyze whether D-GDA leads to flatter loss landscapes. Using trained GCN, we compare D-GDA to Drep FLAGG and LA under Gaussian noise perturbations of model parameters. As shown in Figure D-GDA maintains higher accuracy and lower loss, indicating flatter minima. t-SNE
D-GDA promotes flatter minima for better generalization. Following 86 85
8

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Table 8: D-GDA performance comparison ML safety measures (lower is better). Error is reported on clean data, corruptions are Gaussian (G), Shot (S), Impulse (I), and Shift noise.
Corruptions
Method
Error
Calib,
Consist.
Mean
G
S
Shift
GCN 29
18.40
19.65
16.26
49.42
57.12
54.00
32.60
35,06
+DropEdge
54
18.00
21.16
18.74
62.62
20,90
71.08
19.00
35.38
Cora
+FLAG
24.80
19.52
25.59
33.71
35.17
37.48
31.7
28.41
+1.A 12
15.40
34.33
27.35
63.42
27.68
78.2
27.1
34.47
+D-GDA (ours)
10.9
9.96
15.77
13.34
12.81
16.64
13.59
13.29
GCN 29
28.40
33,43
25.42
46.84
49.90
51.16
40.20
39.34
Citeseer
+DropEdgge
34
28.20
24.14
19.83
70.36
30.9
75.66
29.99
40.38
+FLAG [1
37.30
27.95
25.48
39.08
61.6
56.58
39.7
38.45
+LA 42
25.30
31.44
26.36
68.38
27.98
78.86
26.8
36.44
+D-GDA (ours)
18.5
11.51
21.29
20.52
24.28
20.79
19.36
GCCN 29
21.2
16.74
11.03
45.88
31.26
51.86
33.30
30.18
Pulmedd
+dropEdge
54
22.7
17.47
14.28
50.32
23.64
55.82
21.09
29.33
+FLAG (31
21.5
21.05
9.11
39.64
35.18
59.92
24.29
30.09
+I.A 42
18.3
16.92
10.24
36.00
19.34
46.32
19.30
23.77
+D-GDA (ours)
11.8
8.17
8.13
23.8
15.44
35.72
14.7
16.82
Table 9: Results on adversarial robustness.
Datasets
Method
Clean
Random
DICE
GF-Attack
Meta-Attack
0.00
0,05
0.2
0.05
0.2
0.05
0.2
0.05
0.2
GCN
81.6
78.7
77.2
78.2
74.5
79.8
78.9
79.1
78.4
Coru
+D-GDA
89.1
85.8
83.3
85.7
82.3
85.3
83.9
85.1
83.9
GCN
71.6
64.1
62.6
63.42
60.9
64.9
54.51
63.6
55.13
Citeseer
+D-GDA
81.5
77.9
73.7
77.3
73.4
77.8
72.3
77.5
73.1
Pubmed
78.8
77.9
76
77.6
72.7
77.9
76.1
+D-GDA
88.2
84.4
83.1
83.9
84.2
84.8
82.9
visualizations (Figure show more cohesive, well-separated clusters with D-GDA, further supported by an improved silhouette score (from 0.02 to 0.38). See Appendix B.9 for details.
Sver-Smoothness Analysis. Using MADGap
7 by measuring feature similarity gaps be- tween neighboring and remote nodes: Table 10 shows that D-GDA consistently achieves higher MADGap scores than others (see Appendix B.9 for details).
Ablation Study. Table [1 shows that model per- formance improves as augmentation is applied pro-
Brodal Ch
Jenket Li
Validation Accuracy
(b) Validation Loss
gressively to the training, validation, and test sets, with the best accuracy achieved when all are aug- mented. Validation-set augmentation adds unlabeled synthetic nodes to aid learning in difficult regions, while test-set augmentation serves test-time augmentation by combining predictions from original and augmented nodes. To evaluate the role the GVAE Link Predictor in guiding augmented node connections, compare with three heuristics: Random (target or 1-hop neigh- bor), Target-only, and Target+1-hop. Table T2 shows that our method outperforms all heuristics, highlighting its effectiveness in capturing meaningful structure and boosting classification accuracy. To assess the impact of GVAE Feature Decoder, we replaced it with two heuristics: random features (Rand Feat) and target node features (Target Feat). Both led to notable performance drops (Table 13
Figure 3: D-GDA encourages flatter minima.
Table 10: MADGap Comparison.
Method
Cora
Citeseer
Pubmed
GCN (Vanilla)
0.49
0.53
0.71
+DropEdge
0.41
0.49
0.27
+AdaEdge
0.66
0.53
0.73
#LLAG
0.12
0.17
0.31
(0.02)
GONYD-GBA
+LA
0.49
0.35
+D-DDA
0.64
0.81
0.86
Figure 4: t-SNE of node embeddings on Cora.

---

Table 11: Comparison of augmentation strategies.
Table 12: Importance of proposed link predictor.
Augmentation
Edge injection
Cora
Citeseer
Pubmed
Cora
Citeseer
Pubmed
Val
Test
Random
82.1
72.5
79,4
84.9
80.7
Target
85.3
75.3
80.8
85.8
77.3
83.5
1-hop
83.7
74.5
79.6
88.2
79.8
85.5
89.1
81.5
88.2
Ours
89.1
81.5
88.2
Table 14: Importance of each module in D-GDA
Table 13: Importance of Feature Decoder
Node Features
Cora
Citeseer
Pubmed
TSS
LDM
GVAE
Cora Citeseer
Pubmed
89.1
88.2
Rand Feat
78.6
69.92
75.94
83.5
72.7
80,9
Target Feat
78.8
78.9
71.95
Ours
89.1
81.5
88.2
7
87.3
83.8
79.6
73.5
81.5
85.8
Table 15: Training time and inference time per sample (sec) comparison of D-GDA with baselines.
Cora
Flickr
Ogbn-Arxiv
Type
Method
Train
Inf.
Train
Inf.
Train
Inf.
GCN 29
9.05
0.003
79.82
0.058
928.21
0.567
Non-Diffusion
DdopEdge 54
11.75
0.005
132.23
0.096
1786.40
0.813
FLAG [T
34.20
0.019
547.80
0.160
3307.50
0.815
D-GDA w/o TTA (ours)
37.72
0.019
328.17
0.160
2507 .20
0,816
Diffusion
D-GDA with TTA (ours)
37.72
1.41
328.17
1.33
2507.20 20
1.80
highlighting decoder's role in generating meaningful features and enhancing D-GDA effectiveness. Table [4] assesses the contributions of each module in the D-GDA framework. The full model (TSS + GVAE + LDM) achieves the best performance. Removing TSS leads to a performance drop, high- lighting its role in directing augmentation to challenging regions. Replacing LDM with GVAE results in subpar performance, underscoring LDM's critical role in generating synthetic nodes and edges. Substituting GVAE with GAE also produces lower results. For more ablations see Appendix B.10
Computational Cost Comparison. Table 15| compares the overall training and inference times (in seconds) of D-GDA with and w/o TTA against baseline GCN, and non-diffusion graph data augmentation methods including DropEdge, and FLAG, across three datasets of varying sizes: Cora, Flickr, and Ogbn-Arxiv (large-scale dataset). Note that the execution times of SOTA Diffusion based GDA methods, could not be compared due to non-availability methods, DropEdge consistently demonstrates the lowest training and inference costs, making it the most efficient overall. D-GDA shows better efficiency than FLAG on the larger datasets, Flickr and Ogbn-Arxiv, highlighting its scalability. Additionally, the D-GDA variant without TTA achieves inference times comparable to FLAG, See Appendix B.IT for component-wise training time of D-GDA.
their codes. Among these
5 Conclusions
In this work, we proposed Diffusion-based Graph Data Augmentation (D-GDA), which leverages LDMs to enhance GCN performance, Target Sample Selector (TSS) introduced for identifying challenging-to-tean
samples. Graph Variational Autoencoder (GVAE) is employed for learning com- pact latent representations. We propose neighbourhood based constraint for Latent Diffusion Model (LDM) based node generation. D-GDA enables label-free augmentation applicable to node, edge, and graph-level tasks. Extensive experiments on 14 benchmarks demonstrate D-GDA superiority over the compared SOTA techniques. D-GDA also improves safety measures, including calibration, corruption, consistency, and robustness to adversarial attacks. These results highlight D-GDA's potential as effective and versatile augmentation strategy for advancing graph learning.
Acknowledgement
This work was supported by the International Science and Technology Cooperation Project of Guangzhou Economic and Technological Development District (No. (No.2023GH16), China.
10

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Diffusion-Guided Graph Data Augmentation
Supplementary Material
A How Proposed D-GDA is Different from the Existing SOTA Methods?
Table I6 presents an extended comparison D-GDA against 30 State- Are (SOTA) methods, evaluating key aspects such basic building blocks, supported tasks, robustness assessments, learning settings, and test-time augmentation. It table an extension of Table in the main paper.
Table 16: (Table 1 extension) A comparison of SOTA GDA methods: 1) Basic building blocks: graph auto-encoder (GAE), Graph Variational auto-encoder (GVAE), and Diffusion models. 2) Supported tasks: Node Classification (NC), Link Prediction (LP), and Graph Classification (GC).
3) Robustness evaluations: adversarial robustness (Adv) and machine learning safety measures
(MSM). 4) Learning Settings: semi sumi-supervised, Supervised, and Long-tailed (LT). 5) Best-Time
Augmentation (TTA).
Basic Building Blocks
Supported Tasks
Robustness
Learning Setting
Methods
TTA
GAE
GVAE
Dill.
NC
LP
GC
Adv
MSM
Semi
Sup.
LT
DropEdge
AdaEdge
X
X
X
NodeAug
X
X
X
X
X
GAug 90
X
X
V
X
X
X
X
X
X
Graph Mixup
73
X
X
X
V
X
X
X
V
V
X
ReNode [
X
V
X
X
X
X
X
GraphSMOTE. 87
V
X
X
SR+DR (60]
V
GraphENS
X
J
X
X
FLAG
X
J
X
LA 42
X
X
J
X
X
NASA 3
X
J
X
X
CFLP 89
X
TAM(S-ENS)
59
G-Mixup [8]
GraphSHA 37
DropMessage
X
S-Mixup 26
X
DropEdge++ 17
X
X
GraphPatcher
25
X
iraaphMix 23
X
SkipNode 44
X
X
GeoMix 991
X
RGDA 39
X
X
X
xAI-Drop
X
X
X
DCT 40
X
X
X
LeDA [4
X
GM 63
DoG 7
CCM 52
D-GDA (ours)
B Details of Experiments Performed using Proposed D-GDA
B.1 Datasets' Details
We evaluate our proposed method on four small-scale and two large-scale datasets. Cora, Citeseer, and Pubmed (56) are citation networks where nodes are papers and edges represent citation links. Node features are bag-of ofo-ods representation of papers. Flickr [46) is social network in which nodes are users and edges represent user interaction from an image and video hosting website. OGBN-Arxiv 22 is directed graph, representing the citation network between all Computer Science (CS) arXiv papers. Each node is an arXiv paper and each directed edge indicates that one paper cites another one. Each paper comes with 128-dimensional feature vector obtained by
Node Classification:

---

averaging the embeddings of words in its title and abstract. network having products as nodes and the edge indicates that the products are bought together. Table 17 summarizes the dataset statistics.
[22 is co co-purchasing
Table 17: Summary statistics of node classification evaluation datasets
Datsets
#Nodes
#Edges
#Classes
Train/Valid/Tees split
Cora
2,708
5,278
140/500// (0000000.000 [29
Citeseer
3,327
4,552
6
120/500/1 ,000 29
Flickr
7,575
2,39,738
757/1,5155 5,303
[90
Pubmed
19,717
44,338
3
60/500/1, 0,000
[29
OGBN-Arxiv
169,343
1,166,243
40
1..941//9.799/48.00
22
OGBN-Products
2,449.029
61,859, 140
47
196.615/399333322213....
[22]
We evaluate proposed method on five datasets: ogbl-collab [70 ogbl-ddi [75), Cora, Citeseer, and Pubmed [56]. Ogbl-collab [70] is an undirected collaboration network between authors indexed by MAG. Each node represents an author, and edges indicate collaborations between authors. All nodes have 128-dimensional features, obtained by averaging the word embeddings of papers published by the authors. Each edge is associated with two pieces of inttriinfommtoin: the year and the edge weight, representing the number of co-authored papers published in that year. The task is predict future author collaborations given past collaborations. Ogbl-ddi [75 an undirected graph representing the drug-drug interaction network. Each node represents an FDA-approved or experimental drug, and edges represent interactions between drugs, indicating that the joint effect of taking the two drugs together is significantly different from their independent effects. The task is to predict drug-drug interactions given information on known interactions. Cora, Citeseer, and Pubmed are citation networks. Table [8 summarizes the dataset details.
Link Prediction:
Table 18: Summary Statistics of link prediction evaluation datasets
Datasets
#Nodes
#Edges
#Features
Train/Vall Valn//aalTTstt
Ogbl-collab
235,868
1,285,465
128
92/04/04
[22
Ogbl-ddi
4,267
1,334,889
80/10/10
22
Cora 2.708
5,278
1,433
85/05/10
351
Citeseer
3,327
4,552
3,703
85/05/10
35
Pubmed 19,717
44,338
500
85/05/10
35
We evaluate our proposed method on four molecular property prediction datasets: mggg-R,,, ogbg-ClinToox, ogbg-molHIV, and ogbg-molBACE, (78). Each graph represents a molecule, where nodes are atoms, and edges are chemical bonds. The input node features 9-dimensional, including atomic number, chirality, and additional atom features such formal charge and ring membership. Table summarizes the key statistics for all five datasets.
Graph Classification:
Table 19: Summary Statistics of graph classification evaluation datasets
Datasets
#Graphs
Average #Nodes
Average #Edges
#Classes
Train/Val/ Test
1,427
33.6
70.7
27
80/10/10
gelg-molClin''ee
1,477
26.2
55,8
2
80/10/10
22
Ogbg-molHIV
41.127
25.5
27.5
2
80/10/10
Ogbg-molBACEF 1,513
34.1
73.7
80/10/10
Datasets for Class Imbalance Evaluations: We evaluate our method on the Cora and Citeseer datasets [56] in long-tailed setting. To assess models under conditions of high class imbalance, we create toilet citation networks following the methodology outlined in [10]. This involves adjusting the class distribution to follow long-tailed pattern by systematically removing nodes, thereby increasing the imbalance ratio, which is defined as the ratio between the most frequent class and the least frequent class. achieve this, we sort the classes descending order by size and iteratively remove nodes from each class, starting with the major class. During the node removal process, we prioritize eliminating nodes with low degrees and removing the corresponding edges while striving to maintain graph connectivity. Table 20 summarizes the dataset statistics.

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Table 20: Summary Statistics of Graph Class Imbalance Evaluation Datasets
Datasets
#Nodes
#lidges
#Classes
#Training Nodes Per Class
Cora 2,708
5,278
7
[34. 7. 158, 341, 73, 15, 3]
Citeseer
3,327
4,552
6
[3, 23, 371, 147, 58, 9]
Table 21: (Table extension) Node classification performance comparison D-GDA variants and SOTA methods on small-scale datasets. Best and 2nd best performances are in bold and underline, respectively.
Method
Cora
Flickr
Citeseer
Pubmed
Mean
GCN 22
81.60=0.70 70
61.20=0.40
71.60=0.40
78.80=0.60
73.30
+DropEdge
SE1
82.00=10.80
61.40-1070
71.80+0.20
77.30:10.32
73.13
+AdaEdge 7
81.90=0.70
61.20=10.50
72.80=0.70
77.40=10.50
73.33
+SR+DR 60
83.44=0.34
71.76+00.15
80.64-t0.12
78.61
+NodeAug 80
82. 0..90
7..40
78.80 =0.40
77.43
+GAug[20]
83.60=0.50
62.20-10.30
1.10
80.20=10.30
74.83
+Graph Mixup 73
73.80=10.02
64.30
76.60:10.18
71.57
+FLAG 31
75.20=0.40
62.90-1.200
62.70=1..0
78.50
69.83
+LA 42
84.60=0.50
64.24+10.0
74.70
81.70=#0.70
76.31
+NASA
8..10
+0.40
80.20+00.30
80.30
DrropMessage
13
83.33
53.55-10.23
70.09
79.20+10.06
71.98
+S-Mixup 26
84.78=0.15
74.3910.10
79.70=t0.17
79.62
+DropEdge++ 17
83.10:0.12
63.18
72.70
80.00=10.42
74.75
+GraphPatcher
25
84.17=0.54
71.65
81.13:+0.68
78.98
+xAI-DropFdde
83.60+0.50
+4.00
79.50+0.40
79.03
+iGraphMix 23
83.78=:042
53.61=0.12
73.6710.61
79.93+0.60
72.75
+SkipNode 43
82.00=0.40
50.73=0.09
69.60
77.50
69.96
+GeoMix 91
84.08=0074
0..0
80.06+0.93
79.73
+RGDA 39
84.33
03.0
82.08
79.81
+LeDA 41
78.60+00.2
62.64
0..50
79.70+00.02
72.11
+DoG 7
84.00=10.30
73.60
82.80-L0.30
80.13
+D-GDA (ours)
89.10 0.42
87.30 0.60
81.50
88.20-10.18
86.53
B.2
More Details of Experiments for Node Classification
B.2.1 Experiment Setup and Implementation Details
For TSS, train baseline 2-layer Graph Convolutional Network (GCN) with a hidden dimension of 32, trained using the Adam optimizer with learning rate of 0.001 for 500 epochs. Early stopping applied with patience of 20 epochs prevent overfitting. Next, train Graph Variational Autoencoder (GVAH) to learn latent representation. The GVAF consists of a 2-layer GCN encoder learn node representations and two 2-layer Multi-Layer Perceptrons (MLPs) for decoding edge and feature information, respectively. We set the latent dimension to 64, The GVAE is optimized using composite loss function: LEVAE Ledge + X + >22 where A 0.3 weights the feature reconstruction loss and >₂ = 0.01 controls the KL-divergence term for regularization as recommended by the original authors 30). The GVAE trained for 1000 epochs with the Adam optimizer, using learning rate of 0.01 and weight decay of 5 x 10 10 Following [3 47]. we apply edge masking at rate of 0.3 and feature masking a rate training. Finally, we train Latent Diffusion Model (LDM) with timestep 7 = 1000 and a hidden dimension of 64. The LDM is optimized using the Adam optimizer with learning rate of 1 x 10-1 for 1000 epochs, generating high-quality augmented samples for the node classification task.
to enhance robustness during

---

B.2.2 Improvementss over GCN backbone
Table 21 presents comprehensive comparison of D-GDA against existing SOTA methods using the GCN backbone. Across all evaluated datasets, D-GDA consistently outperforms both the baseline GCN and the second-best SOTA method, demonstrating significant performance improvements.
B.2.3 Improvements over GAT backbone
We evaluate the performance of D-GDA on the Graph Attention Network (GAT) backbone [67 using three benchmark citation network datasets: Cora, Citeseer, and Pubmed. Table 22 presents comparative analysis of D-GDA against existing SOTA methods under the GAT architecture. D- GDA achieves substantial performance gains over both the baseline GAT model and current SOTA approaches. Specifically, D-GDA outperforms the GAT baseline by 8. 8.1%, 8.5%, and 9.5%, and exceeds the previous SOTA performance by 4.7%, 4.3%, and 9.1% on Cora, Citeseer, and Pubmed, respectively. Given that GAT is a self-attention-baseee highly sensitive to both graph connectivity and node features, the observed improvements highlight the effectiveness and compatibility of the augmentation strategies introduced by D-GDA within attention-based architectures.
model, where performance is known to be
Table 22: (Table Mablensextesion Node classification performance comparison of D-GDA using additional backbones including GAT (67 and GSAGE [16].
Method
Cora
Citeseer
Pubmed
Vanilla
81.3
70.5
79.4
+DropEdge 154
81.9
71.0
79.6
AAdaFdge 7
82.0
71.1
76.6
+SR+DR [60
83.5
72.4
79.4
+NodeAug [80]
84.1
70.8
78.3
+GAug [90]
82.2
71.6
79.3
GAT
+LA [42]
84.7
74.7
79.8
+DropMessage
82.2
71.5
78.1
+xAI-DropEdge
82.6
72.8
78.8
+iGraphMix
23
83.2
72.3
78.4
+L.DD 41
83.5
72.1
79.5
+SkipNode 43
81.6
68.4
77.6
+D>GIDA (ours)
89.4
79.0
88.9
Vanilla
81.3
70.6
76.8
+DropEdge
54
81.6
70.8
77.1
+AdaEdge
81.5
71.3
77.2
GSAGE
+NodeAug 80
82.2
70.2
78.1
+GAug 990
83.2
72.7
78.5
+LeDA 41
82.2
72.3
77.6
NokipNode
81.5
68.5
77.4
+RGDA [39
83.4
72.6
82.1
+D-DDA (ours)
88.7
80.2
89.5
B.2.4 Improvements over GSAGE backbone
We evaluate the performance of D-GDA using GSAGE (Graph SAmple and aggreGatE) [16] backbone using three benchmark datasets, including Cora, Citeseer, and Pubmed. In Table 22 we compare results with existing SOTA methods GSAGE backbone. D-GDA consistently improves both baseline GSAGE and SOTA methods. Specifically, D-GDA outperforms the GSAGE baseline by 7.4%, 9.6%, and 7.4%, and exceeds the previous SOTA performance by 5.3%, 7.5%, and 7.4% Cora, Citeseer, and Pubmed, respectively.
B.3 Implementation Details for Link Prediction
To enhance data augmentation for link prediction tasks, for TSS, we train 2-layer Graph Convolutional Network (GCN) with hidden dimension of 32 to generate node embeddings, followed by simple

---

Table 23: (Table extension) Balanced accuracy (%) comparison under class imbalance ratio of
100.
Method
Cora-LT
Citeseer-LT
GCN (Vanilla)
59.42-+0.74
44.64+00.42
+Reweight
78.42+t0.10
63.61#0.22
+cRT
76.54+0.22
60.60::0.25
+PC Softmax
77.30=t0.13
62.15=0.45
+CB Loss
77.97:10.19
61.47:0.551
+ Focal Loss
78.43:10.19
59.66+10.38
ReNode
67.61+0.113
47.78+0031
Upsample
7..52++0.11
55.05+0.11
+DR-GCN
73.90+:.29
56.18=1.100
+GraphSMOTE
87
66.29+:0.43
44.40=10.29
+GraphENS 49
70.31
55.42:10.35
+TAM (G-ENS)
(59
72.10+0.23
57.15+0.34
+GrppSHA [3
74.62+00229
59.04=0.41
+GraphVCM
52
75.81+0.42
6..53
+D-GDA (ours)
80.34
64.9510.11
dot product to predict links. is trained using the Adam optimizer with learning rate 0.001 for 1000 epochs, incorporating early stopping with patience of 20 epochs to prevent overfitting. For all link prediction datasets, we set augmentation budget in the Target sample selector (TSS) to 20% of total number of training links for all datasets. The GVAE and LDM for link prediction trained with the same parameters as those used for node classification.
B.4 Implementation Details for Graph Classification
To enhance data augmentation for graph classification tasks, begin by training Target Sample Selector (TSS) to identify the most informative graphs for augmentation. The TSS employs 2- layer GCN with hidden dimension of 32 compute node embeddings, which subsequently aggregated into graph-level representations using a mean readout layer. The model is optimized using the Adam optimizer with learning rate of 0.001 and trained for up 1000 epochs, employing early stopping with a patience of 20 epochs to mitigate overfitting. For all graph classification datasets, we set augmentation budget in the Target sample selector (TSS) to 20% of total number of training graphs for all datasets. This targeted approach ensures augmentation focuses on samples with the highest potential impact. The GVAE and LDM used for augmentation are trained with the same hyperparameters as those employed in the node classification setting.
B.5 Extended Experiments for Class Imbalance Handling Methods
The TSS, GVAE, and LDM components follow the same training procedures described in the node classification setup (Section B.2).
B.5.1
Extended comparison with SOTA Methods
Table 23 provides an extended comparison of D-GDA with existing SOTA methods for handling class imbalance in the node classification task. This table serves as an extension of Table 7 presented in the main paper.
B.5.2 Imbalance Ratio Analysis
The Imbalance Ratio (IR) is defined as the ratio of the sample size of the largest majority class to that of the smallest minority class [10]. with higher IR values indicating more severe class imbalance. Many existing graph imbalance handling methods attempt to mitigate this by generating synthetic nodes for classes to match the majority class
49 thereby balancing the training data. However, such approaches often introduce unnecessary complexity and may lead to overfitting. In contrast, D-GDA effectively reduces class imbalance without enforcing class-level symmetry generating synthetic nodes across all classes. At the of D-GDA is the Targeted Sample
5

---

Selector (TSS), which identifies the nodes, regardless of their class, that are most likely to benefit from augmentation. This class-agnostic selection enables more natural and targeted correction of imbalance. As result, D-GDA leads to significant reduction in the imbalance ratio. For instance, the IR drops from 113.67 to 19.55 on Cora, and from 123.67 to 14.6 on Citeseer, as shown in Table
24
Table 24: Comparison of the augmentation budget (AugBudget) for reducing class imbalance ratio
(IR) using D-GDA and SOTA methods.
Datasets
Methods
#Training Nodes per Class
IR
AugBudget
Original Data
134, 7, 158, 341, 3I
113.67
Cora
SOTA (Table 22) Augmentation
341,, 341, 341, 341, 3411
278%
D-GDA Augmented Data
[85, 160, 391, 78, 39, 20]
19.55
26.4%
Original Data
[3, 23, 147, 58, 9] 371, 371, 371]
123.67
Citeseer
SOTA (Table 22) Augmentation
264%
D-GDA Augmented Data
[30, 66, 438, 208, 66, 36]
14.6
38.13%
B.6 D-GDA Improvements in ML Safety Measures (More Details)
We evaluate D-GDA across three key machine learning (ML) safety measures, including calibration, corruption robustness, and consistency, using three widely adopted benchmark datasets: Cora, Citeseer, and Pubmed. Table in the main paper summarizes the results. All models are trained on clean versions of the datasets, i.e., the original data for the GCN baseline, and augmented versions for D-GDA and other GDA baselines. Performance is then assessed across the aforementioned safety tasks. Below, we define each safety measure, describe its objective, and provide details on the corresponding evaluation metrics.
Calibration: The goal the calibration task classify nodes with calibrated prediction probabili- ties, i.e. matching the empirical frequency of correctness. In other words, model that predicts with 80% confidence should be correct approximately 80% of the time. To evaluate this, we use the Root
Mean Squared (RMS) Calibration Error 20 defined as: v E.(((PY = ЙIC = c) c)a]. where C
the classifier confidence that it's prediction is correct. We compute the RMS calibration error using 15 bins estimate the empirical accuracy different confidence levels.
The objective of this task is to evaluate model robustness by classifying corrupted test nodes, with performance measured using the mean classification errоr. We assess D-GDA under four types feature corruption: Gaussian noise, shot noise, impulse noise, and feature shift. Following the protocol from [19]. apply five severity levels the Gaussian (G), shot (S), and impulse (I) noise corruptions to simulate varying degrees degradation. For the feature shift corruption, we randomly select 10% of the test nodes and replace their features with those of randomly chosen one-hop neighbor. It is important to emphasize that only test node features are corrupted, and the model is never trained corrupted data. Below, include the Python code used to generate these corrupted node features.
Corruption:
def gaussian noise noise severity=1): [0.04, 0.06, .08, .09, .10] [severity 1]
2
return feature np. np. random. normal normal (eazur shape, scale-c)
def shot_noise (feature, severity=1): = [500, 250, 100, 75, 50] [severity 1]
return np random. poisson(featur c)
9 def impulse moieeeeoooieeeeeeeeeeeeeeeeeeeee (aaallee,niseefeauuuee,e (feature, severity=1): [.01, .02, .03, .05, .07] [severity 1]
10 return sk. util. random. noise (feature, mode- 'skp', amount=c)
def shift (node, features, adj):

---

one_order_nee _ei adj [node] monzero () [1]
15
neighbors up append order_nee node)
16
swap_with random choice
17
corr_feat features (aatures.clon(()
corr_feat [node], corr_ [swap_with] corr_ [swaa__wwitt
corr_ [node]
return corr corr_feat
This task evaluates a model's ability to consistently classify similar versions of the same test node. For each node, create sequence S containiig the original node's features and several perturbed versions with increasing noise levels. The goal is for the model to predict the same class for all nodes within sequence S, even as the features become progressively noisier. We denote m perturbation sequences with [-] 22 2n ). Following [19], we set = 31. measure consistency, we use the mean flip rate (mFR), as defined in Eq. 2 The mFR corresponds to the probability that adjacent nodes within sequence increasing noise levels have different predicted classes.
Consistency:
mFR
S n 1) i= 1 + #((x
m
where, f() is the trained classifier and is the original unperturbed features. Below is the Python code to obtain sequence original features.
def get_sqquence (features, n-31);
seq []
for in range(1, n+1)):
randn_lanneeeeeeeeee___aalle features - features + 0.02 randn, like (feature)))
seq append (features)
return seq 6
B.7 D-GDA Adversarial Robustness Analysis (More Details)
To evaluate the robustness of D-GDA against adversarial attacks, employ four well-established evasion attacks: Random (random edge flips), DICE [74] (removes intra-class edges and adds inter-class edges), GFAttack 66) (optimizes low-rank loss generate structural perturbations), loss maximization). Each attack is applied at two perturbation levels, with perturbation ratios (a 0.05, 0.2). All attacks conducted under evasion attack setting, where the graph structure is perturbed only at test time, leaving the training data unchanged. For GCN, the model is trained
and Meta-attack [93] (uses meta-gradient-ban
clean data, whereas D-GDA is trained using
its graph-augmented data. We leverage the GreatX: Graph Reliability Toolbox [3] to generate the ad adversarially perturbed graphs. Table in the main paper summarizes the results.
(a) Validation Accuracy
(b) Validation Loss
(c) GCN (-0.06)
(d) GCN+D-GNDD GDA (0.18)
Figure 5: Citeseer dataset: (a) and (b): D-GDA promotes flatter minima in the loss landscape. (c) and (d): t-SNE visualizations of node embeddings, demonstrating improved class separability with D-GDA. Silhouette score is shown in parenthesis.

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B.8 D-GDA Robustness to Homophily
The node homophily defined as the average fraction of node's neighbors that share the same label [50]. Table 25] compares these node homophily scores with GCN and D-GDA performance, well as the resulting performance gain across six node classification and three link prediction datasets. Pearson's correlation coefficient between node homophily and these performances is computed. We observe a positive correlation of 0.63 between homophily and GCN performance, however, a reduced correlation of 0.45 with D-GDA performance. It suggests that D-GDA performance is not strongly correlated with homophily compared to GCN. More interestingly. we observe negative correlation of -0.37 between homophily and performance gain of D-GDA, indicating that D-GDA performance gain is robust to homophily. On the remaining datasets, node labels are not available, so homophily not be computed.
Table 25: Node Homophily Vs GCN and D-GDA performance: The D-GDA performance gain is robust homophily. Downstream Task
Datasets
Node Homophily
GCN
D-GDA
Performance Gain
Cora
0.83
81.6
89.1
9.19
Flickr
0.67
61.2
87.3
42.65
Node Classification
Citeseer
0.72
71.6
81.5
13.83
Pubmed
0.79
78.8
88.2
11.93
Ogbn-Arxiv
0.63
71.62
74.8
4.44
Ogbn-Produse
0.83
71.37
78.85
10.48
Cora
0.83
89.55
96.96
8.27
Link
Citeseer
0.72
69.47
93.72
34.91
Prediction
Puhmed
0.79
96.11
97.82
1.78
Pearson's Correlation
0.63
0.45
-0.37
B.9
More insights to the improvements obtained by D-GDA
B.9.1 D-GDA promotes flatter minima for enhanced generalization
In addition to the Cora dataset results in the main paper, we evaluate D-GDA on the Citeseer and Pubmed datasets. Using trained GCN, compare D-GDA against DropEdge, FLAG, and LA under Gaussian noise perturbations model parameters. As shown in Figure aa). D-GDA achieves higher accuracy and lower loss (Figure ()) Citeseer, indicating flatter minima that enhance generalization. t-SNE visualizations (Figure and (d)) reveal more cohesive and well-separated clusters for D-GDA, with the silhouette score improving from -0.06 to 0.18. A similar trend is observed on Pubmed (Figure 6). where the silhouette score increases from 0.13 to 0.34, further confirming D-GDA's ability promote robust and generalizable representations.
400
600
(a) Validation Accuracy
(b) Validation Loss
(c) GCN (0.13)
(d) GCN+D-GDA (0.34)
Figure 6: Pubmed dataset: (a) and (b): D-GDA promotes flatter minima in the loss landscape. (c) and (d): t-SNE visualizations of node embeddings, demonstrating improved class separability with
D-GDA. Silhouette score is shown in parenthesis.
B.9.2 Oversmoothness analysis using MADGap measure (More Details)
To quantify the smoothness of graph representations, we employ the MADGap measure, as described by Chen al. [7]. The results are presented in Table of of the main paper. Below, outline the T0ble/o0ol

---

MADGap measure and its computation. The Mean Average Distance (MAD) assesses graph represen- tation smoothness by computing the average distance between nodes. Given graph representation matrix H E Raxd' (where d' is the hidden dimension of the final GNN layer), we first calculate the distance matrix D E Rax= using the cosine distance between all node pairs. We then filter target node pairs by element-wise multiplication with a mask matrix M to obtain D = D M The average distance for each row in Dist is computed as:
Σ DY=0 D
En === (
where 1(-) is the indicator function. The MAD score for the target node pairs is then calculated by averaging the non-zero D values:
25=0 D Digt
MAD
My (D)
Using the graph topology to approximate node categories, we compute the MADGap to evaluate oversmoothness:
MADGap MAD MAD
(5)
where MAD is the MAD for remote nodes (order 2 8) and MAD is the MAD for neighboring nodes (order I 3). large positive MADGap indicates that nodes receive more useful information than noise, reflecting appropriate smoothing and good GNN performance. Conversely, a small or negative MADGap suggests oversmoothing, leading to degraded performance.
B.9.3 Test-Time Time Consistency and Diversity (More Details)
To evaluate the quality of augmented data, we adopt the consistency and diversity metrics proposed by Bo et al. [3] and extend them to the test set. We train two models, Fi and Fe Rd - R on the original training data Drain and augmented data Denin. respectively, where d is the input feature dimension, is the number of classes, and 0 represents the learnable parameters. Both models are then used predict on the test set D Effective augmentations should enable Fg to achieve higher test accuracy and establish a distinct decision boundary compared to Fe.
Time Consistency: We measure consistency the accuracy of the augmented model on the test set, defined as Crest Fco(Fo( Yuea), where Yes denotes the test data labels. A low Cres indicates that the augmentations are inconsistent with the original data, potentially reducing model accuracy. However, a high Cust does not necessarily imply high- qugh-qualtt augmentations, as it may reflect limited generalization.
To assess diversity, we compute the difference between the predictions of the original and augmented models using the Frobenius norm: Diest = |i (Deel) - Fo (Deaa)))
Test-Time Diversity:
low Diest suggests that the augmented data closely resembles the original data, offering little benefit to model generalization (Yin et al., 2019). Conversely, high Drest does not guarantee correct augmentations, as may introduce noise.
A robust augmentation strategy should balance high consistency (Cuet) and sufficient diversity (Diest to ensure both accuracy and improved generalization. Figure 7 illustrates the trade-off between diversity and consistency for D-GDA compared to existing SOTA augmentation methods. Across all datasets, D-GDA achieves a favorable balance between the two, suggesting that its performance gains may stem from this effective trade-off.
B.10
Additional Ablations
In this section, present additional ablation studies beyond those in the main paper to provide clearer understanding of various design choices.
B.10.1 Impact of Neighborhood Aggregation Method on Performance
To assess the impact of different neighborhood aggregation strategies, we experiment with two commonly used methods: mean and max aggregation. These strategies are used to compute the con- ditioning vector oi for augmentation generation. As shown in Table 26 the mean aggregation yields

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DCS
I-ODA
GOS
+LA. Bidoss
Tolfee
Teogtddy
Droplidge
LeDA
F1A0
CC%
Drupbdde
Tadts
FLAG
(a) Cora
(b) Flickr
(c) Citeseer
oot
DACIAN
UKS
GCTX
sttmphorr
LA APLAGG
-FLAG
#TLAG
<ladt
Too Coeieenc
Hick
GUN
1A
0..6
PLAG
Depplige
Despitiee
Drcpdig:
Tervenhhiskty
(d) Pubmed
(c) Ogbn-ArXiv
(f) Products
Figure 7: (Details of Figure 1b
Diversity vs. consistency comparison six datasets. Methods
falling in top-right corner shows good balance of diversity vs. consistency
superior performance, indicating its effectiveness in capturing relevant neighborhood information for guiding the augmentation process.
Table 26: Impact of Neighborhood Aggregation Method on Performance
Aggregation Method Max Mean (ours)
Cora
Citeseer
Pubmed
87.5
78.8
84.7
89.1
81.5
88.2
B.10.2 Impact of Multi-Hop Neighborhood Condition on Performance
To assess the effect of multi-hop neighborhood condition on model performance, we conducted an ablation study by modifying the conditioning vector of in the LDM to incorporate embeddings from 1-hop, 2-hop, and 3-hop neighboring nodes. The results, summarized in Table 27 show decline in performance neighborhood depth increases. This may be attributed to the changing class labels of nodes in deeper neighborhoods, which could prevent the synthetic node features from accurately capturing the target class's 's characteristics. Notably, depicted in Figure & increasing the neighborhood depth enhances test-time diversity but reduces test-time consistency.
D--DRA (ishpp) ciscssssalu
Tast-ut Comvistrncyy
D-GDA (I-hup)
Table 27: Impact Multi-hop Neighborhood Ag- gregation on overall performance.
D-GIM (2-hop)
Conditioned On
Cora
Citeseer
Pubmed
1-hop neighbors (ours)
89.1
81.5
88.2
DD-GA (3-hop)
80
2-hop neighbors
88.2
79,9
87.9
20
12
3-hop neighbors
86.8
77.6
85.3
Thetsert Divenity
Figure 8: Multi-hop Neighborhood impact on test-time consistency and diversity
10

---

B.10.3 Node Importance Selection Strategies for Graph Classification
To evaluate the effectiveness of the proposed degree-based node selection method, we compared it against two alternative strategies including random selection and PageRank-based selection. Table summarizes the results for graph classification across these strategies. Following [15], compute PageRank with damping factor of 0.85 the proposed degree- barree selection consistently outperforms both alternatives. This supports the intuition that high-degree nodes are indeed more structurally influential, reinforcing the effectiveness of degree-bast based selection the optimal strategy in our setting.
convergence tolerance of 10 We observe that
Table 28: D-GDA performance comparison on graph classification datasets using the proposed degree- based node selection strategy, compared against random and PageRank- selection methods.
Node Selection Strategy ogbg-molSIDER oglg ogbg-molHHI ogbg-molBACE Random node
61.19
89.98
77.42
75.68
Page-rank top-node
63.24
92.76
78.83
81.92
Highest degrec node (ours)
64.85
94.82
79.03
83.45
B.10.4 Effectiveness Test Time Augmentation (Extended Evaluation)
We present an extended evaluation Test Time Augmentation (TTA) by expanding the analysis to 10 datasets to provide more comprehensive view. Table 29 summarizes the results for GCN and D-GDA, both with and without TTA, along with the per-sample TTA cost. Across all datasets and tasks, observe consistent performance improvements when employing TTA, highlighting its generalizability and effectiveness.
Table 29; Performance comparison of GCN and D-GDA with and without test time augmentation
(TTA) along with Per-sample inference time (sec) with TTA
GCN
D-GDA
TTA
Inference Cost/Sample
Datasets
w/o TTA
with TTA
TTA
with TIA
Time/Sample
Cora
81.6
83.2
88.2
89.1
1.39
1.41
Flickr
61.2
64.01
84.65
87.3
1.17
1.33
Citeseer
71.6
73.37
79.2
81.5
1.53
1.55
Pubmed
78.8
80.41
85.5
88.2
1.21
1.23
Ogbn-Arxiv
71.62
72.52
72.7
74.8
0.98
1.8
Ogbn-Products
71.37
72.85
77.60
78.85
1.02
1.94
Ogbg-MolSIDER
59.6
61.08
62.92
64.85
0.96
1.08
Ogbg-molCIin Tox
88.55
89.92
91.8
94.82
0.97
1.11
Ogbg-molHil
76.06
77.63
77.9
79.03
0.96
1.09
Ogbg-molBACE 71.47
73.26
79.24
83.45
0.95
1.06
B.10.5 Ablation Different Choices of Target Sample Selection (TSS) Backbones
In D-GDA, TSS identifies difficult samples based on prediction entropy. To maintain consistency, the same backbone architecture in TSS in the downstream model being evaluated. For example, when comparing D-GDA performance with a GCN backbone, we also use GCN within TSS; similarly, for GAT or GraphSAGE, the corresponding backbone used in both components. The rationale behind this design that each GNN backbone employs a different message passing mechanism, and result, node that may appear difficult for model may not be difficult for another architecture. Table 30 summarizes the results of using GCN, GAT, and GraphSAGB within the TSS module across multiple experiments. The findings show that the best performance is consistently achieved when the same backbone is used in both TSS and the downstream classifier, confirming the importance of the proposed choice of architecture in TSS.
B.10.6 Hyperparameter Analysis
To evaluate the influence of hyperparameters the overall performance of D-GDA, we conduct an ablation study focusing on the weighting parameters X₁ and A in the GVAE loss function using Cora, Citeseer, and Pubmed datasets for the node classification task. The parameters X and X2
11

---

Table 30: Ablation on different choices of TSS backbones.
Downstream Backbone
TSS Backbone
Cora
Citeseer
Pubmed
GCN
89.1
81.5
88.2
GCN
GAT
87.8
79.8
85.5
GSAGE
87.4
80.2
85,4
GCN
86.2
76.2
87.1
GAT
GAT
89.4
79.0
88.9
GSAGE
87.3
78.4
86.8
GCN
86.7
77.5
85.8
GSAGE
GAT
87.3
78.9
86.1
GSAGE
88.7
80.2
89.5
regulate the trade-off between feature reconstruction and latent space regularization, both of which are critical for generating high-quality augmented graph data. this ablation, we systematically vary Å E (031, 3.5) and X2 E {0.01, 0.05, 0.1}. while keeping all other components of D-GDA unchanged. For each pair of A and 22 values, we train the GVAE to generate augmented graphs, which subsequently used train the node classification model. Table 31 presents the results, reporting classification performance across different hyperparameter configurations. The analysis highlights the sensitivity of GVAE to the balance between feature reconstruction and regularization. For example, increasing Å emphasizes feature reconstruction, which can improve node-level fidelity but may lead overfitting. Conversely, higher A2 values impose stronger regularization the latent space, promoting stability but potentially reducing the model's capacity to capture nuanced structural information.
Table 31: Hyperparameter Analysis
A1
X2
Cora
Citeseer
Pubmed
0.01
88.38
79.92
86.45
0.1
0,05
85.5
75.36
84.68
0.1
82.28
72.83
81.73
0.01 (ours)
89.1
81.5
88.2
0.3 (ours)
0.05
87.12
79.8
87.02
0.1
82.52
73.86
84.7
0.01
88.56
80.13
87.14
0.5
0.05
85,23
78.25
84.88
0.1
82.48
74.6
81.92
B.11 D-GDA Training Time Breakdown
Table 32
provides a component-wisg breakdown of the D-GDA training time, covering Traget Sample Selector (TSS), Graph Variational Autoencoder (GVAF), and Latent Diffusion Model (LDM), along with its inference time with Test-Time Augmentation (TTA). Training and inference time are reported using a 4x A16 GPU machine with 128GB RAM.
B.12 D-GDA Scalability and Efficiency Analysis
Table 33 compares the scalability of D-GDA across datasets of varying numbers of nodes and number of graphs. Specifically, performance gain, training time, and per-sample inference time of D-GDA are compared with the dataset size. datasets containing multiple graphs, we report the average number of nodes per graph. The results demonstrate that D-GDA scales efficiently with increasing dataset size. The training time increases sublinearly as the dataset size increases, while still delivering significant performance improvements over GCN.
B.13 Limitations of the Proposed D-GDA Algorithm
potential limitation of the proposed D-GDA framework is its training time computational cost and test-time memory overhead. It requires training GCN baseline, GVAE, and LDM for each dataset.
12

---

Table 32: Training (sec) and Inference time per sample (sec) component breakdown of the
proposed D-GDA framework.
Train Time
Inference Time
Datasets
TSS
GVAE+LDM
Data Aug+Training
Total
TTA
Inference
Total
Cora
9.35
12.82
15.55
37.72
1.39
0.019
1.41
Flickr
79.87
85.13
163.17
328.17
1.17
0.16
1.33
Citeseer
11.67
17.86
18.32
47.85
1.53
0.021
1.55
Pubmed
40.01
43.62
145,79
229.42
1.21
0.024
1.23
Ogbn-Arxiv
728.86
774.92
903.42
2407.2
0.98
0.816
1.8
1253.84
1548.24
1698.23
4500.31
1.02
0.92
1.94
MoRS
95.11
105.32
113.72
314.15
0.96
0.12
1.08
oghg-molClinTTox Tox
96.32
106.46
116.24
319.02
0.97
0.14
1.11
ogbg-mollHIV
572.28
585.18
596.48
1753.94
0.96
0.13
1.09
ogbg-molBACE
96.84
103.92
114.62
315.38
0.95
0.114
1.06
Table 33: Scalability analysis of D-GDA with varying graph sizes (number of nodes IVI and number of graphs IGI), showing performance gains over the baseline GCN, along with total training and inference times (in seconds). D-GDA exhibits sublinear growth in training time with increasing dataset size.
Datasets
M
IGI
Gain
Inf.
Time
Train Time
Train Time Per Sample
Cora
2,708
9.19
1.41
37.72
0.0139
Flickr
7.575
42.65
1.33
328.17
0.0433
Citeseer
3327
13.83
1.55
47.85
0.0144
Pubmed
19,717
11.93
1.23
229.42
0,0116
Ogbn-Arxiv
169,343
4.44
1.8
2407.2
0,0142
Ogbn- Products
2,449,029
10.48
1.94
4500.31
0.0018
ogbg-molSIDEr
33.6
1,427
8.81
1.08
314.15
0.2201
ogbg-molCling Tox
26.2
1,477
7.08
1.11
319.02
0.216
25.5
41,127
3.9
1.09
1753.94
0.0426
molBEEE
34.1
1,513
16.76
1.06
315.38
0.2084
This process resource-intensive than some traditional augmentation methods, such as DropEdge. However, some traditional methods such as FLAG have also shown similar computational time. Being diffusion based framework, D-GDA requires GVAE and LDM during inference if test-time augmentation is employed. Without test-time augmentation its inference time remains almost the same as existing SOTA methods. Despite the higher computational overhead, the substantial performance improvements over SOTA methods justify the additional cost, making D-GDA a compelling choice for high-quality graph data augmentation.
C Convergence Proof of LDM in D-GDA Framework
We provide theoretical justification for the convergence of LDM in the D-GDA framework setting, which operates in label-free settings. Despite the inherent challenges of sparse graph supervision, we show that the denoising network in D-GDA converges the true conditional score function, enabling to sample augmentations from a neighborhood-awwe foundational results from score-based generative modeling (21 62 611, adapted to the graph setting with local structural conditioning. Let v; denote node in graph G (V,& E), with latent representation 2 (R)d obtained from Graph Variational Autoencoder (GVAE). We assume a standard DDPM- style forward process that gradually corrupts 20 with Gaussian noise. The reverse process aims estimate the noise via a denoising network (0(2,, t, c..), conditioned on a neighborhood-awar vector c. The model is trained with score-match motee-matching loss: L E.g.t.llc co(2), e For details See Section 3.1.3. Our goal is to show that under mild assumptions, the denoising model converges to the true conditional score function of the local latent distribution, enabling realistic and diverse augmentations without reliance class labels. We begin by stating the following assumptions:
latent distribution. Our analysis follows the
Assumption (Locality Assumption): The latent variable 2! drawn from a smooth conditional distribution p(2)) [u;)), supported on a low-dimensional manifold.
13

---

Table 34: Impact of reducing training data for LDM on training loss, validation loss, early stopping epoch, and node classification accuracy. Training Data Percentage
Performance Metric
Cora
Citeseer
Pubmed
Ogbn-Arxiv
Train Loss
0.069
0,084
0.077
0.068
100%
Val Loss
0.153
0.176
0.249
0.251
Test Acc.
89.1
81.5
88.2
74.8
Train Loss
0.059
0.064
0.067
0.057
60%
Val Loss
0.178
0.197
0.275
0.307
Test Acc.
86.8
79.2
86.4
73.1
Train Loss
0.029
0.034
0.042
0.032
40%
Val Loss
0,203
0.236
0.319
0.324
Test Acc.
82.3
75.6
81.9
71.8
Assumption 2 (Model Capacity): The denoising network eo is a universal approximator i.e. has enough expressive power to learn any function within given function class (For D-GDA the score function of the noisy latent distribution).
Assumption 3 (Difflusion Schedule): The noise schedule {a, is chosen such that är + 0 as + XC, ensuring near-total corruption at the final step.
Theorem 1: Let ea(2), t, <)) be trained using the denoising score matching objective, Then, as + oc and model capacity increases, 6g converges to the conditional score function: ea cs(2,, ft cf)) + V # log Pz c,), where (z | c.") is the marginal distribution of the noisy latent variable at time t, conditioned on the local structure node e4-
Sketch of Proof: This result follows from established results in score-based generative modeling [1]. Minimizing the denoising score-matching loss recovers the true score function of the noisy data distribution. In D-GDA, the conditioning vector ef restricts generation node's 's local neighborhood, simplifying the modeling of p(2 (u;)) as a smooth, low-dimensional conditional distribution. Assumption A1 ensures the score function is well-defined and smooth, while Assumption A2 guarantees that Ep can approximate this function arbitrarily well. The noise schedule in A3 ensures that the diffusion process sufficiently corrupts the latent code, enabling meaningful denoising learning. Together, these yield convergence to the true conditional score function. This theoretical justification confirms that D-GDA's latent diffusion process, when conditioned local neighborhood structure, can provably learn a brighborhood-awar augmentation distribution, without requiring access to class labels.
Empirical validation: we evaluate D-GDA's LDM under increasingly limited training data. Specifi- cally, we reduce the amount of training data from 100% to 60% and 40%, and track LDM behavior across four graph datasets: Cora, Citeseer, Pubmed, and Ogbn-Arxiv. Early stopping is applied based on validation loss with patience of 10 epochs. In Table 34 report the training loss, validation loss, early stopping epoch, and D-GDA test accuracy. We observe that, as the training data decreases, training loss consistently decreases (e.g., Cora: 0.069 to 0.029), due to easier overfitting fewer samples. Validation loss increases (e.g.. Pubmed: 0.249 - 0.319), indicating reduced generalization from limited training data. LDM trained with less data tend converge earlier (e.g., Ogbn-Arxiv: 672 + 172), suggesting faster overfitting. Test accuracy drops across datasets (e.g., Citeseer: 81.5% 75.6%), the model struggles generate diverse augmentations.
14


Reviews:
[{"review_id": "WK82X0sD1S", "reviewer": "Reviewer_vgsq", "summary": "The authors introduce a new framework for graph augmentation, applicable to all common graph tasks of graph classification, link prediction and node classification. It is based on three main components 1) target sample selector, that selects nodes/edges to augment 2) a GVAE that encodes/decodes the graph to a latent space and 3) a latent diffusion model that augments the embeddings and thus the graph. The method is tested on common benchmarks for this three tasks and shows improvement over other augmentation techniques. It also helps model robustness.", "questions": "Please see the last two paragraphs (weaknesses) above. \n\nOne additional question is did you consider other node importance selection strategies for graph classification. Like page rank or just random selection. Degree-based selection certainly makes sense intuitively, but it would be nice to know if it's indeed the optimal choice.", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Traditional graph augmentation techniques have historically been lacking. And to make them successful you needed to make them domain specific. Using a generative approach is a neat way to avoid having to hand-craft them. The three components introduced are all quite sensible and follow current best generative model approaches (latent diffusion). The TSS using a baseline model to find hard nodes is nice and sensible idea, that is ablated/shown to work with in-silico experiments. In general the paper provides extensive experimental evidence and the results are very good. In both making the downstream GCN more robust and more accurate.\n\nThe method uses neighborhood embeddings as conditioning when denoising the augmented node. For graph classification the most important nodes are taken to be highest degree nodes. Both are sensible choices, but conceptually they do correlate with homophily, and most datasets used (especially link prediction and node classification ones) are quite homophilous. It would be interesting to know if improvements over base GNN correlate with how homophilous the dataset is, or if the method is robust to this.\n\nAs I understand test time augmentation is used in all experiments. It does make the method much more expensive than other competitors and judging by table 14 it is a crucial part of methods performance. This however is quite similar to model ensambling, so it would be good to see how it stacks up with simple model ensambling and/or what the results would be for the rest of the datasets (link prediction and graph classification) if no test time augmentation would be used, as computational expense wise that's closer to the baselines.", "was_revised": true, "final_justification": "The authors addressed all the main points I raised in the initial review and I think now it is a well rounded paper.", "rebuttal": "# D-GDA Robustness to Homophily\n\nThe **node homophily** is defined as the average fraction of a node’s neighbors that share the same label [R1]. Table 1 compares these node homophily scores with GCN and D-GDA performance, as well as the resulting performance gain across six node classification and three link prediction datasets. Pearson’s correlation coefficient between node homophily and these performances is computed. We observe a positive correlation of 0.63 between homophily and GCN performance, however, a reduced correlation of 0.45 with D-GDA performance. It suggests that D-GDA performance is not strongly correlated with homophily compared to GCN. More interestingly, we observe a negative correlation of -0.37 between homophily and performance gain of D-GDA, indicating that D-GDA performance gain is robust to homophily. On the remaining datasets, node labels are not available, so homophily can not be computed. \n\n**Table 1: Node Homophily Vs GCN and D-GDA performance:** The D-GDA performance gain is robust to homophily.\n\n|Downstream Task| Datasets | Node Homophily| GCN |D-GDA|D-GDA performance gain over GCN|\n|-----------|-----------|-----------|-----------|-----------|-----------|\n|Node Classification|Cora |0.83 |81.6 |89.1| 9.19|\n|Node Classification|Flickr|0.67|61.2|87.3|42.65|\n|Node Classification|Citeseer|0.72|71.6|81.5|13.83|\n|Node Classification|Pubmed|0.79|78.8|88.2|11.93|\n|Node Classification|Ogbn-Arxiv|0.63|71.62|74.8|4.44|\n|Node Classification|Ogbn-Products|0.83|71.37|78.85|10.48|\n|Link Prediction|Cora |0.83|89.55|96.96|8.27|\n|Link Prediction|Citeseer|0.72|69.47|93.72|34.91|\n|Link Prediction|Pubmed|0.79|96.11|97.82|1.78|\n||**Pearson’s Correlation**|-|0.63|0.45|-0.37|\n\n[R1] *Platonov, Oleg, et al. \"Characterizing graph datasets for node classification: Homophily-heterophily dichotomy and beyond.\" Advances in Neural Information Processing Systems 36 (2023): 523-548.*\n\n# Test Time Augmentation Effectiveness and Computational Cost Analysis\n\nWe have shown the effectiveness of Test Time Augmentation (TTA) in Table 11 of the main paper. Now we present an extended evaluation by expanding the analysis to 10 datasets to provide a more comprehensive view. Table 2 summarizes the results for GCN and D-GDA, both with and without TTA, along with the per-sample TTA cost. Across all datasets and tasks, we observe consistent performance improvements when employing TTA, highlighting its generalizability and effectiveness. \n\n**Table 2:** Performance comparison of GCN  and D-GDA with and without test time augmentation (TTA).  Per-sample inference time (sec) with TTA is also reported.\n\n| Datasets | GCN w/o TTA| GCN with TTA |D-GDA w/o TTA|D-GDA with TTA|TTA cost/sample|Total inference time/sample|\n|-----------|-----------|-----------|-----------|-----------|-----------|-----------|\n|Cora |81.6|83.2|88.2|89.1|1.39|1.41|\n|Flickr|61.2|64.01|84.65|87.3|1.17|1.33|\n|Citeseer|71.6|73.37|79.2|81.5|1.53|1.55|\n|Pubmed|78.8|80.41|85.5|88.2|1.21|1.23|\n|Ogbn-Arxiv|71.62|72.52|72.7|74.8|0.98|1.8|\n|Ogbn-Products|71.37|72.85|77.60|78.85|1.02|1.94|\n|Ogbg-molSIDER|59.6|61.08|62.92|64.85|0.96|1.08|\n|Ogbg-molClinTox|88.55|89.92|91.8|94.82|0.97|1.11|\n|Ogbg-molHIV|76.06|77.63|77.9|79.03|0.96|1.09|\n|Ogbg-molBACE|71.47|73.26|79.24|83.45|0.95|1.06|\n\n\n# Ablation on Node Importance Selection Strategies for Graph Classification\n\nTo evaluate the effectiveness of the proposed degree-based node selection method, we compared it against two alternative strategies including random selection and PageRank-based selection as suggested. Table 3 summarizes the results for graph classification across these strategies. Following [R2], we compute PageRank with a damping factor of 0.85 and a convergence tolerance of $1 \\times 10^{-6}$. We observe that the proposed degree-based selection consistently outperforms both alternatives. This supports the intuition that high-degree nodes are indeed more structurally influential, reinforcing the effectiveness of degree-based selection as the optimal strategy in our setting.\n\n**Table 3:** D-GDA performance comparison on graph classification datasets using the proposed degree-based node selection strategy, compared against random and PageRank-based selection methods.\n\n|Node selection strategy| ogbg-molSIDER | ogbg-molClinTox| ogbg-molHIV |ogbg-molBACE|\n|-----------|-----------|-----------|-----------|-----------|\n|Highest degree node|**64.85**|**94.82**|**79.03**|**83.45**|\n|Random node|61.19|89.98|77.42|75.68|\n|Page-rank top-node |63.24|92.76|78.83|81.92|\n\n[R2] *Hagberg, A. A., Schult, D. A., & Swart, P. J. (2008). Exploring network structure, dynamics, and function using NetworkX. In Proceedings of the 7th Python in Science Conference (SciPy2008), 11–15.*"}, {"review_id": "K6ui8ctD08", "reviewer": "Reviewer_wrnB", "summary": "This paper studies the research problem of graph data augmentation (GDA), with the aim of developing a task-agnostic GDA method. The authors proposed a diffusion-based approach, namely D-GDA. D-GDA has three main components: Target Sample Selector (TSS), a Graph Variational Autoencoder (GVAE), and a Latent Diffusion Model (LDM), where the diffusion happens on the latent space within the GVAE. Interestingly, with the help of TSS, the proposed method can sample the most valuable samples for augmentation when given a fixed data augmentation budget.", "questions": "I'm mainly curious about how actually this method scales, as well as how efficient it is.", "limitations": "see the weakness and question above.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "s1. The paper overall is clearly written and easy to follow. \n\ns2. The authors conducted very thorough experiments over many benchmarks against many baseline methods. The experiments showcased the effectiveness of the proposed method.\n\ns3. The design around augmenting with a fixed budget is interesting, and could be useful in real applications.\n\nw1. While the authors argued around efficiency given the designs of TSS and test-time augmentation in the proposed method, the efficiency is still concerning considering the method design. There were also no experiments such as run-time comparison of the proposed method against baselines. Such evaluation, especially on larger scale benchmarks, would help showcasing on this perspective.", "was_revised": true, "final_justification": "Thanks for the additional results in the rebuttal! I think they help a lot on the understanding of the proposal's efficiency, and would recommend the authors to add them in the paper.", "rebuttal": "# D-GDA Computational Comparison with Baselines\nTable 4 provides a component-wise breakdown of the D-GDA training time, covering TSS, GVAE, and LDM, along with its inference time with Test-Time Augmentation (TTA). Table 5 compares the overall training and inference times (in seconds) of D-GDA with and w/o TTA against baseline methods including GCN, DropEdge, and FLAG, across three datasets of varying sizes: Cora, Flickr, and Ogbn-Arxiv (large-scale dataset). Among these methods, DropEdge consistently demonstrates the lowest training and inference costs, making it the most efficient overall. D-GDA shows better efficiency than FLAG on the larger datasets, Flickr and Ogbn-Arxiv, highlighting its scalability. Additionally, the D-GDA variant without TTA achieves inference times comparable to FLAG. \n\n**Table 4:** Breakdown of training time (in seconds) and per sample inference time (in seconds) for D-GDA across ten datasets of varying scales.\n\n|Datasets| TSS Train Time| GVAE+LDM Train Time | Data Aug+Training Time|D-GDA Total Train Time|TTA Generation Cost|Inference Time with TTA|D-GDA Total Inference Time|\n|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|\n|Cora|9.35|12.82|15.55|37.72|1.39|0.019|1.41|\n|Flickr|79.87|85.13|163.17|328.17|1.17|0.16|1.33|\n|Citeseer|11.67|17.86|18.32|47.85|1.53|0.021|1.55|\n|Pubmed|40.01|43.62|145.79|229.42|1.21|0.024|1.23|\n|Ogbn-Arxiv|728.86|774.92|903.42|2407.2|0.98|0.816|1.8|\n|Ogbn-Products|1253.84|1548.24|1698.23|4500.31|1.02|0.92|1.94|\n|ogbg-molSIDER|95.11|105.32|113.72|314.15|0.96|0.12|1.08|\n|ogbg-molClinTox|96.32|106.46|116.24|319.02|0.97|0.14|1.11|\n|ogbg-molHIV|572.28|585.18|596.48|1753.94|0.96|0.13|1.09|\n|ogbg-molBACE|96.84|103.92|114.62|315.38|0.95|0.114|1.06|\n\n\n**Table 5:** Training time (sec) and inference time per sample (sec) comparison of D-GDA with baselines.\n\n|Methods| Cora Train Time| Cora Inference Time | Cora Performance|Flickr Train Time| Flickr Inference Time|Flickr Performance |Arxiv Train Time| Arxiv Inference Time | Arxiv Performance|\n|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|\n|GCN|9.05|0.003|81.6|79.82|0.058|61.2|928.21|0.567|71.62|\n|DropEdge|**11.75**|**0.005**|82.0|**132.23**|**0.096**|61.4|**1786.4**|**0.813**|56.26|\n|FLAG|*34.2*|*0.019*|75.2|547.8|*0.16*|62.9|3307.5|*0.815*|71.75|\n|D-GDA with TTA|37.72|1.41|**89.1**|*328.17*| 1.33|**87.3**|*2507.2*|1.8|**74.8**|\n|D-GDA w/o TTA|37.72|*0.019*|*88.2*|*328.17*|*0.16*|*84.65*|*2507.2*|0.816|*72.7*|\n\n# D-GDA Scalability and Efficiency Analysis\nTable 6 compares the scalability of D-GDA across datasets of varying numbers of nodes and number of graphs. Specifically, performance gain, training time, and per-sample inference time of D-GDA are compared with the dataset size. For datasets containing multiple graphs, we report the average number of nodes per graph. The results demonstrate that D-GDA scales efficiently with increasing dataset size. The training time increases sublinearly as the dataset size increases, while still delivering significant performance improvements over GCN.\n\n**Table 6:** Scalability of D-GDA with varying graph sizes. D-GDA training time increases sublinearly with increasing dataset size. \n\n|Datasets|No. of Nodes| No. of Graphs |D-GDA performance gain over GCN| D-GDA Inference Time |D-GDA Training Time| Per Sample Training Time | \n|-----------|-----------|-----------|-----------|-----------|-----------|-----------|\n|Cora|2,708|1|9.19|1.41|37.72|0.0139|\n|Flickr|7,575|1|42.65|1.33|328.17|0.0433|\n|Citeseer|3327|1|13.83|1.55|47.85|0.0144|\n|Pubmed|19,717|1|11.93|1.23|229.42|0.0116|\n|Ogbn-Arxiv|169,343|1|4.44|1.8|2407.2|0.0142|\n|Ogbn-Products|2,449,029|1|10.48|1.94|4500.31|0.0018|\n|ogbg-molSIDER|33.6 |1,427|8.81|1.08|314.15|0.2201|\n|ogbg-molClinTox|26.2|1,477|7.08|1.11|319.02|0.216|\n|ogbg-molHIV|25.5|41,127|3.9|1.09|1753.94|0.0426|\n|ogbg-molBACE|34.1|1,513|16.76|1.06|315.38|0.2084|"}, {"review_id": "5M0uI1YuTg", "reviewer": "Reviewer_MRas", "summary": "This paper proposes a Graph Data Augmentation (GDA) method called D-GDA, which is based on Graph Variational Autoencoder (GVAE) and Latent Diffusion Model (LDM). The framework consists of three key components: i). Target sample selection（TSS）, ii). Graph variational auto-encoder（GVAE）, and iii) Latent Diffusion.  In addition, D-GDA is model-agnostic and label-free, making it highly flexible for various applications. Extensive experiments demonstrate its effectiveness.", "questions": "Please refer to the weaknesses.", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n\n1. The framework of D-GAD is sample and model-agnostic, enabling it enabling it to be applied more flexibly.\n\n2. D-GDA not only focuses on performance improvement in the GDA scenario but also conducts research on model security.\n\n3. The experiments compare performance across multiple tasks with numerous baseline models and ample benchmark datasets, providing comprehensive and thorough comparative analysis.\n\nWeaknesses：\n\n1. This paper lacks a structured theoretical description of TSS, GVAE, and LDM in the Methodology section(Sec. 3), which hinders a clear understanding of the technical approach.\n\n2. GDA is inherently designed for scenarios with sparse or restricted graph data. However, LDM's convergence requires large amounts of data and significant computational resources. A theoretical proof of LDM's convergence in the current D-GDA setting is necessary.\n\n3. D-GDA appears to primarily integrate existing techniques (e.g., GVAE, LDM) into the DGA scenario. The paper should further emphasize the description of its technical innovations.", "was_revised": true, "final_justification": "My concerns have been addressed , and I have increased both the Clarity and Final Rating scores to 3 and 4, respectively.", "rebuttal": "# 1) Section 3 Revision\nWe have thoroughly revised the theoretical descriptions of TSS, GVAE, and LDM in the methodology section (Section 3) to improve the structure and understanding of the proposed D-GDA framework.\n\n# 2a) LDM Convergence Proof\nWe provide a theoretical justification for the convergence of LDM in the  D-GDA framework setting, which operates in label-free settings. Despite the inherent challenges of sparse graph supervision, we show that the denoising network in D-GDA converges to the true conditional score function, enabling it to sample augmentations from a neighborhood-aware latent distribution. Our analysis follows the foundational results from score-based generative modeling [20, R3, R4], adapted to the graph setting with local structural conditioning. Let $v_{i}$ denote a node in graph $\\mathcal{G} = (\\mathcal{V}, \\mathcal{E})$, with latent representation $z_{i}^{0} \\in \\mathcal(R)^{d}$ obtained from a Graph Variational Autoencoder (GVAE). We assume a standard DDPM-style forward process [20] that gradually corrupts $z_{i}^{0}$ with Gaussian noise. The reverse process aims to estimate the noise via a denoising network $\\epsilon_{\\theta}(z_{i}^{t}, t, c_{i}^{0})$, conditioned on a neighborhood-aware vector $c_{i}^{0}$. The model is trained with a score-matching loss ($\\mathcal{L_{diff}}$).  For details See Section 3.1.3. Our goal is to show that under mild assumptions, the denoising model $ ε_{\\theta}$ converges to the true conditional score function of the local latent distribution, enabling realistic and diverse augmentations without reliance on class labels. We begin by stating the following assumptions:\n\n**Assumption 1 (Locality Assumption):** The latent variable $z_{i}^{0}$ is drawn from a smooth conditional distribution $p(z_{i}^{0} \\mid \\mathcal{N}(v_{i}))$, supported on a low-dimensional manifold.\n\n**Assumption 2 (Model Capacity):** The denoising network $ε_{\\theta}$ is a universal approximator i.e. has enough expressive power to learn any function within a given function class (For D-GDA the score function of the noisy latent distribution).\n\n**Assumption 3 (Diffusion Schedule):**  The noise schedule $\\\\{\\alpha_{t}\\\\}$, where $t$ varies from $1 \\to T$, is chosen such that $\\bar{\\alpha}_{T} \\to 0$ as $T \\to \\infty$, ensuring near-total corruption at the final step.\n\n**Theorem 1:** *Let $ε_{\\theta}(z_{i}^{t}, t,c_{i}^{0})$ be trained using the denoising score matching objective. Then, as $T \\to \\infty$ and model capacity increases, $ε_{\\theta}$ converges to the conditional score function: $ε_{\\theta}(z_{i}^{t}, t,c_{i}^{0}) \\rightarrow \\nabla_{z_{i}^{t}} \\log p_{t}(z_{i}^{t} \\mid c_{i}^{0}) $, where $p_{t}(z_{i}^{t} \\mid  c_{i}^{0})$ is the marginal distribution of the noisy latent variable at time $t$, conditioned on the local structure of node $v_{i}$.*\n\n**Sketch of Proof:** This result follows from established results in score-based generative modeling [R3]. Minimizing the denoising score-matching loss recovers the true score function of the noisy data distribution. In D-GDA, the conditioning vector $c_i^0$ restricts generation to a node's local neighborhood, simplifying the modeling of $p(z_i^0 \\mid N(v_i))$ as a smooth, low-dimensional conditional distribution. Assumption A1 ensures the score function is well-defined and smooth, while Assumption A2 guarantees that $\\epsilon_\\theta$ can approximate this function arbitrarily well. The noise schedule in A3 ensures that the diffusion process sufficiently corrupts the latent code, enabling meaningful denoising learning. Together, these yield convergence to the true conditional score function. This theoretical justification shows that D-GDA's latent diffusion process, when conditioned on local neighborhood structure, can provably learn a neighborhood-aware augmentation distribution, without requiring access to class labels. \n\n**Empirical Validation:** We evaluate D-GDA’s LDM under increasingly limited training data. Specifically, we reduce the amount of training data from 100\\% to 60\\% and 40\\%, and track LDM behavior across four graph datasets: Cora, Citeseer, Pubmed, and Ogbn-Arxiv. Early stopping is applied based on validation loss with a patience of 10 epochs. In  Table 7, we report the training loss, validation loss, early stopping epoch, and D-GDA test accuracy. We observe that, as the training data decreases, training loss consistently decreases (e.g., Cora: 0.069 to 0.029), due to easier overfitting on fewer samples. Validation loss increases (e.g., Pubmed: 0.249 $\\to$ 0.319), indicating reduced generalization from limited training data. LDM trained with less data tend to converge earlier (e.g., Ogbn-Arxiv: 672 $\\to$ 172), suggesting faster overfitting. Test accuracy drops across datasets (e.g., Citeseer: 81.5\\% $\\to$ 75.6\\%), as the model struggles to generate diverse augmentations.\n\n**Table 7:** Impact of reducing training data for LDM on training loss, validation loss, early stopping epoch,  and node classification accuracy\n\n|Training Data Percentage|Performance Metric|Cora|Citeseer|Pubmed|Ogbn-Arxiv|\n|-----------|-----------|-----------|-----------|-----------|-----------\n|100%|Train Loss|0.069|0.084|0.077|0.068|\n|100%|Val Loss|0.153|0.176|0.249|0.251|\n|100%|Test Acc.|89.1|81.5|88.2|74.8|\n|60%|Train Loss|0.059|0.064|0.067|0.057|\n|60%|Val Loss|0.178|0.197|0.275|0.307|\n|60%|Test Acc.|86.8|79.2|86.4|73.1|\n|40%|Train Loss|0.029|0.034|0.042|0.032|\n|40%|Val Loss|0.203|0.236|0.319|0.324|\n|40%|Test Acc.|82.3|75.6|81.9|71.8|\n\n[R3] *Song, Yang, et al. \"Score-based generative modeling through stochastic differential equations.\" arXiv preprint arXiv:2011.13456 (2020).*\n\n[R4] *Song, Yang, and Stefano Ermon. \"Generative modeling by estimating gradients of the data distribution.\" Advances in neural information processing systems 32 (2019).*\n\n# 2b) D-GDA Training and Inference Cost Breakdown\nTable 8 provides a component-wise breakdown of the D-GDA training time, covering TSS, GVAE, and LDM, along with its inference time with Test-Time Augmentation (TTA). For comparison of computational time with compared methods please see Table in rebuttal.\n\n**Table 8:** Breakdown of training time (in seconds) and per sample inference time (in seconds) for D-GDA across ten datasets of varying scales\n\n|Datasets| TSS Train Time| GVAE+LDM Train Time | Data Aug+Training Time|D-GDA Total Train Time|TTA Cost|TTA Inference Time|D-GDA Total Inference Time|\n|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|\n|Cora|9.35|12.82|15.55|37.72|1.39|0.019|1.41|\n|Flickr|79.87|85.13|163.17|328.17|1.17|0.16|1.33|\n|Citeseer|11.67|17.86|18.32|47.85|1.53|0.021|1.55|\n|Pubmed|40.01|43.62|145.79|229.42|1.21|0.024|1.23|\n|Ogbn-Arxiv|728.86|774.92|903.42|2407.2|0.98|0.816|1.8|\n|Ogbn-Products|1253.84|1548.24|1698.23|4500.31|1.02|0.92|1.94|\n|ogbg-molSIDER|95.11|105.32|113.72|314.15|0.96|0.12|1.08|\n|ogbg-molClinTox|96.32|106.46|116.24|319.02|0.97|0.14|1.11|\n|ogbg-molHIV|572.28|585.18|596.48|1753.94|0.96|0.13|1.09|\n|ogbg-molBACE|96.84|103.92|114.62|315.38|0.95|0.114|1.06|\n\n\n\n# 3) Description of Technical Innovation\nOur technical innovation lies in the utilization of GVAE and LDM for the task of graph data augmentation. Specifically, how these components are adapted, extended, and algorithmically integrated for the graph data augmentation is novel. D-GDA is a cohesive, task-adaptive framework with novel mechanisms and substantial empirical gains. The technical contributions of D-GDA include:\n\n**Target Sample Selector (TSS):** A novel component that selects samples that would benefit the most from the augmentation based on prediction entropy. TSS utilization results in improved  (See Table 14 in main paper)\n\n**Neighborhood-aware Latent Diffusion Model (LDM):** We propose to adapt LDM to the graph domain by applying the diffusion process in the latent space learned by GVAE, while explicitly modeling local graph structure. This design allows for generating high-quality node representations that preserve both feature and topological context. Removal of LDM results in reduced performance, as shown in Table 14.\n\n**Multi-task Compatibility:** Unlike prior works that target a single setting, D-GDA is versatile and effective across node classification, link prediction, and graph classification, as well as in semi-supervised, supervised, and long-tailed settings.\n\n**ML Safety Measures:** D-GDA is shown to improve critical safety measures such as calibration, robustness to adversarial attacks, and improved performance under feature corruption. These evaluations go beyond traditional accuracy benchmarks and highlight the practical utility and robustness of our proposed D-GDA framework."}, {"review_id": "IrUHin5BfX", "reviewer": "Reviewer_N1DJ", "summary": "The paper proposes Diffusion-Guided Graph Data Augmentation (D-GDA), a novel framework to enhance the performance and generalization of Graph Neural Networks (GNNs) by generating diverse and consistent graph augmentations. The key components of D-GDA include Target Sample Selector (TSS), Graph Variational Autoencoder (GVAE) and Latent Diffusion Model (LDM).\n\nThe method is task-agnostic and label-free, enabling test-time augmentation. Extensive experiments on 12 benchmarks show superior performance over 30 SOTA methods, with improvements in generalization, robustness to adversarial attacks, and ML safety measures.", "questions": "See weakness.", "limitations": "Yes.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. The paper introduces a label-free, diffusion-based GDA framework applicable to multiple graph tasks, unlike prior task-specific methods.\n2. Neighborhood-aware conditioning ensures augmentations preserve local structure while diversifying data.\n\nWeaknesses:\n\n1. The paper claims to balance diversity and consistency in augmentations but does not explicitly define how these metrics are measured. Are they based on feature variance or some other criterion?\n2. While diversity and consistency are highlighted as key advantages, the paper does not explain why these metrics matter and whether they conflict (e.g., more diversity may reduce consistency).\n3. The TSS relies on a baseline GNN to identify \"difficult\" samples via entropy. However, the choice of baseline architecture (e.g., GCN or GraphSAGE) may bias sample selection. Is this evaluated? \n4. The paper claims lower computational costs due to latent-space diffusion but does not provide theoretical analysis or empirical benchmarks. Without these, the efficiency claims remain unsubstantiated. \n5. The method is described as using a Graph Variational Autoencoder (GVAE), but the cited work refers to Variational Graph Autoencoders (VGAE). Is this a terminological inconsistency or a modified architecture?", "was_revised": true, "final_justification": "Thank you for your detailed response. The author has addressed all of my concerns thoroughly, and I am pleased to revise my rating accordingly.", "rebuttal": "# 1) Definition and Measurement of Consistency and Diversity\nThe definitions of consistency and diversity [3], along with how to measure them, have already been provided in Supplementary Section B.8.3; however, we will revise the main paper to explicitly reference this section for clarity. Specifically, **Consistency** is measured as the test accuracy of the model trained on augmented data, reflecting how well the augmentation preserves task-relevant semantics, and **Diversity** is measured as the Frobenius norm of the difference between the prediction logits of the original and augmented models, capturing how much variation the augmentation introduces in the model’s outputs. For more details, please refer to Supplementary Section B.8.3.\n\n# 2) Importance of Consistency and Diversity\nConsistency and diversity [3, R5, R6] are used as key indicators for measuring augmentation quality. Consistency ensures that augmentations preserve task-relevant semantics, leading to stable predictions. Diversity encourages variations that expose the model to different structural or feature-level perturbations, promoting better generalization. While these objectives can indeed conflict (i.e., excessive diversity may harm consistency), an effective augmentation strategy must balance both to avoid overfitting to trivial perturbations or being too invariant to informative changes. In our work, we demonstrate that existing methods tend to lean towards one of these at the expense of the other (Figure 1b). In contrast, D-GDA is able to strike a good balance between both.\n\n[R5] *Juan, Xin, et al. \"Multi-strategy adaptive data augmentation for Graph Neural Networks.\" Expert Systems with Applications 258 (2024): 125076.*\n\n[R6] *Chen, Nan, et al. \"Consistency training with learnable data augmentation for graph anomaly detection with limited supervision.\" The twelfth international conference on learning representations. 2024.*\n\n# 3) Ablation on different Choices of Target Sample Selection (TSS) Backbones\nIn D-GDA, TSS identifies difficult samples based on prediction entropy. To maintain consistency, we use the same backbone architecture in TSS as in the downstream model being evaluated. For example, when comparing D-GDA performance with a GCN backbone, we also use GCN within TSS; similarly, for GAT or GraphSAGE, the corresponding backbone is used in both components. The rationale behind this design is that each GNN backbone employs a different message passing mechanism, and as a result, a node that may appear difficult for one model may not be difficult for another architecture. Table 9 summarizes the results of using GCN, GAT, and GraphSAGE within the TSS module across multiple experiments. The findings show that the best performance is consistently achieved when the same backbone is used in both TSS and the downstream classifier, confirming the importance of the proposed choice of architecture in TSS.\n\n**Table 9:** Ablation on different choices of TSS backbones.\n\n|Downstream Backbone| TSS Backbone |Cora| Citeseer|Pubmed|\n|-----------|-----------|-----------|-----------|-----------|\n|GCN|GCN|**89.1**|**81.5**|**88.2**|\n|GCN|GAT|87.8|79.8|85.5|\n|GCN|GSAGE|87.4|80.2|85.4|\n|GAT|GCN|86.2|76.2|87.1|\n|GAT|GAT|**89.4**|**79.0**|**88.9**|\n|GAT|GSAGE|87.3|78.4|86.8|\n|GSAGE|GCN|86.7|77.5|85.8|\n|GSAGE|GAT|87.3|78.9|86.1|\n|GSAGE|GSAGE|**88.7**|**80.2**|**89.5**|\n\n# 4) Diffusion Model and Latent Diffusion Model (LDM) Computational Cost Comparison\nRombach et al. [R7] demonstrated that training a state-of-the-art diffusion model requires approximately 1000 V100 GPU-days, whereas training a Latent Diffusion Model (LDM) reduces this cost to just 271 V100 GPU-days, reflecting a 3.6× improvement in training time. This computational advantage of LDMs has been consistently highlighted in prior works such as [5, 20, 66]. We outline our rationale for adopting latent diffusion in Section 3.1.3 of the main paper. Specifically, Latent Diffusion Models (LDMs) offer a significantly more efficient and tractable alternative to applying diffusion directly in the raw feature space. Especially for graph data, training diffusion models in the raw feature space presents two key challenges: 1) **High-dimensional sparsity: ** Many graph datasets, such as Cora and Citeseer, contain sparse and high-dimensional feature vectors. Modeling directly in this space makes diffusion model training unstable and computationally expensive. 2) **Structural complexity:** Preserving both topological and semantic information during diffusion model training in the raw space demands more complex architectures and heavier training models, further increasing the resource burden. \n\nTo overcome these issues, our method applies diffusion in a compact latent space learned via our Graph Variational Autoencoder (GVAE). This latent representation captures the essential structural and feature-level information while significantly reducing dimensionality and sparsity. As a result, latent diffusion not only lowers computational cost but also enhances training stability and scalability. We will revise the manuscript to more clearly communicate this motivation to further strengthen the theoretical grounding of our design choice. In Table 14 main paper, removal of LDM resulted in reduced performance on three datasets.\n\n[R7] *Rombach, Robin, et al. \"High-resolution image synthesis with latent diffusion models.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2022.*\n\n# 5) Clarification between VGAE and GVAE \nWe cited VGAE [29] as it introduced the foundational concept of applying variational autoencoders to graph-structured data. However, our use of the term GVAE (Graph Variational Autoencoder) reflects a generalized and modified architecture beyond what VGAE originally proposed. Specifically, VGAE was designed for link prediction and employs a dot-product decoder that only reconstructs edge presence. In contrast, our GVAE includes two distinct decoders: a feature decoder that reconstructs node features, and an edge decoder that reconstructs edge connectivity. Please see Section 3.1.2 for more details."}]

Author rebuttal:

Meta-review: The reviewers unanimously recommend acceptance of the paper with varying degrees of strength. I agree with their assessment and am happy to recommend acceptance of this paper for publication at the NeurIPS conference. 

The reviews and the rebuttal have given rise to several interesting points and results that I encourage the authors to include in their revised manuscript. I believe the Final Remark posted by the authors to summarise these points nicely, and do want to encourage the authors to make all the edits and inclusions corresponding to the eight points they summarise. Finally, I also strongly want to encourage the authors to make their code publicly available together with the camera ready version (and to adjust the abstract of their paper accordingly).
Decision: Accept (poster)