Structural Entropy-Driven Graph Diffusion Generation for One-Shot Federated Graph Learning

Shutong Zheng; Lele Fu; Sheng Huang; Wei Yang Bryan Lim; Chuan Chen

cs.LGSep 6, 2026

Structural Entropy-Driven Graph Diffusion Generation for One-Shot Federated Graph Learning

Authors: Shutong Zheng, Lele Fu, Sheng Huang, Wei Yang Bryan Lim, Chuan Chen

Organizations: Sun Yat-sen University Guangzhou, China · Nanyang Technological University Singapore

Abstract

One-shot federated graph learning (FGL) requires the server to estimate client contributions from highly compressed information, yet conventional volume-based weighting captures the amount of client data while overlooking how its connectivity is organized. In this paper, we propose SPIRE, a Structural Entropy-Driven Graph Diffusion Generation method that introduces topology-aware client differentiation into one-shot FGL. Specifically, we employ first-order degree-distribution structural entropy as a compact descriptor of degree-mass dispersion and use it to derive structural client weights, providing an inductive bias that accounts for differences in graph topology beyond data volume. On the generation side, a graph diffusion model on the server synthesizes pseudographs conditioned on the weighted client prototypes, capturing both semantic and structural information without requiring additional client-side training. The generated pseudographs are then assembled via disjoint union fusion to train a global graph neural network. Extensive experiments on seven real-world graph datasets demonstrate that SPIRE consistently outperforms conventional and one-shot FGL methods, with particularly strong gains under highly heterogeneous (non-IID) and graph-perturbed settings.

Figures & tables

Figure 1. Illustration of the volume–structure mismatch in client weighting. C1 is a large “Noisy Giant” (800 nodes), while C2 is a smaller “Clean Expert” (169 nodes) with differentiated community structure; C3–C5 follow standard non-IID partitions. FedAvg favors C1 by volume, whereas SPIRE differentiates client influence using structural entropy.

Figure 2. Controlled decoupling of client volume and topology on Cora. Four client archetypes independently vary graph volume and degree-distribution entropy, revealing distinct local utilities.

Figure 3. Overview of SPIRE. Clients upload structural entropy, class prototypes, and node counts in a single communication round. The server performs structural-entropy-based weighting, Wasserstein Barycenter initialization, pseudograph generation, and global GNN training.

Type	Methods	Cora	CiteSeer	PubMed	Amz-Comp	WikiCS	Coauthor-CS	ogbn-arxiv
BL	FedAvg [AISTATS17]	34.74	36.08	61.92	37.70	19.47	25.33	14.58
FL	FedProx [MLSys20]	28.24 ↓6.50	30.48 ↓5.60	54.62 ↓7.30	24.74 ↓12.96	4.22 ↓15.25	23.33 ↓2.00	13.37 ↓1.21
	FedOPT [ICLR21]	29.68 ↓5.06	21.82 ↓14.26	43.86 ↓18.06	12.42 ↓25.28	10.57 ↓8.90	7.76 ↓17.57	2.14 ↓12.44
	MOON [CVPR21]	27.98 ↓6.76	22.12 ↓13.96	45.50 ↓16.42	23.71 ↓13.99	4.13 ↓15.34	11.44 ↓13.89	11.57 ↓3.01
FGL	FedProto [AAAI22]	30.50 ↓4.24	24.56 ↓11.52	52.86 ↓9.06	37.66 ↓0.04	6.67 ↓12.80	26.51 ↑1.18	5.20 ↓9.38
	FedPub [ICML23]	21.16 ↓13.58	19.16 ↓16.92	41.16 ↓20.76	37.70 ↓0.00	17.49 ↓1.98	8.51 ↓16.82	10.16 ↓4.42

Table 1. Performance comparison on node classification tasks. The abbreviations in the first column denote: BL (Baseline), and OS (One-shot Federated Learning). The best results are highlighted in bold , and the second-best results are underlined . The small numbers indicate the performance gap compared to FedAvg (

\uparrow

improvement,

\downarrow

degradation).

Methods	Cora	CiteSeer	PubMed	ogbn-arxiv
FedAvg (200 rounds)	65.71 s / 2814 MB / 66 s	67.33 s / 7246 MB / 68 s	66.45 s / 984 MB / 67 s	79.17 s / 330 MB / 80 s
GHOST [ICML25]	40.36 s / 16.0 MB / 71 s	60.00 s / 38.0 MB / 102 s	5471 s / 7.0 MB / 5716 s	18106 s / 3.0 MB / 20028 s
OASIS [NeurIPS25]	172 s / 44.0 MB / 179 s	179 s / 111 MB / 189 s	6971 s / 17.0 MB / 7004 s	OOM
SPIRE (Ours)	<0.01 s / 0.38 MB / 1265 s	<0.01 s / 0.85 MB / 1227 s	<0.01 s / 0.06 MB / 986 s	0.11 s / 0.20 MB / 653 s

Table 2. Efficiency and Communication Overhead Comparison. Each cell presents Comm. Time / Comm. Cost / Total Training Time .

T_{train}

for SPIRE includes server-side diffusion training, while others denote cumulative training time.

Panel of Figure 4 — Figure 4. Impact of data heterogeneity ( $\beta\in[0.05,0.25]$ ) on datasets Cora and Citeseer.

Methods	Cora	CiteSeer	PubMed	ogbn-arxiv
(a) Edge Perturbation ( $\rho=0.5$ )
FedAvg	31.90 ↓2.84	18.10 ↓17.98	42.40 ↓19.52	22.28 ↑7.70
DENSE	16.40 ↓8.70	18.20 ↓0.16	41.60 ↓0.10	3.48 ↓2.38
FedCVAE	15.10 ↑0.32	17.20 ↑0.03	41.00 ↑7.32	21.56 ↑10.04
FedSD2C	14.90 ↓6.78	16.90 ↓1.76	41.20 ↑8.30	7.87 ↑2.00
GHOST	32.75 ↓5.44	40.60 ↑1.65	48.94 ↓10.09	17.54 ↑2.01

Table 3. Robustness analysis under edge/feature perturbation (

\rho

\eta

0.5

) on representative datasets of varying scales. The small numbers indicate the performance deviation compared to the clean setting (

\uparrow

improvement,

\downarrow

degradation).

Dataset	Method	$K=5$	$10$	$20$	$50$	$100$
Cora	FedAvg	32.40	34.74	31.90	32.31	31.95
	GHOST	41.54	38.19	34.15	37.10	35.33
	OASIS	51.56	41.66	35.42	40.59	37.59
	SPIRE	55.70	64.06	57.70	60.35	58.58
PubMed	FedAvg	60.80	61.92	63.40	61.80	59.35
	GHOST	60.52	59.03	56.37	57.35	58.37

Table 4. Scalability under severe data fragmentation (

\beta=0.05

) with varying numbers of clients

K

. Best results are bold.

Panel of Figure 5 — Figure 5. Hyperparameter Analysis on $\lambda_{se}$ and $\lambda_{align}$ on Cora.

Datasets	(a) Core Architecture Ablation				(b) Generative Refinements
	Baseline	+ SE	+ GFM	SPIRE	w/o WB	w/o Jitter	w/o $\bm{\gamma(s)}$
	Baseline	(w/o GFM)	(w/o SE)	(Full Model)	(SE+GFM+Jit+ $\gamma$ )	(SE+GFM+WB+ $\gamma$ )	(SE+GFM+WB+Jit)
Cora	39.20	44.20 ↑5.00	59.80 ↑20.60	64.06 ↑24.86	59.40 ↓4.66	62.33 ↓1.73	63.79 ↓0.27
CiteSeer	29.90	41.90 ↑12.00	47.90 ↑18.00	55.32 ↑25.42	50.50 ↓4.82	53.75 ↓1.57	52.50 ↓2.82
PubMed	63.20	67.30 ↑4.10	69.70 ↑6.50	73.40 ↑10.20	70.30 ↓3.10	71.90 ↓1.50	72.15 ↓1.25
Amz-Comp	34.75	35.90 ↑1.15	37.30 ↑2.55	38.32 ↑3.57	37.70 ↓0.62	36.79 ↓1.53	36.50 ↓1.82

Table 5. Ablation study of SPIRE across seven datasets. Panel (a) evaluates the foundational impact of the core components. Panel (b) assesses the internal generative refinements via removal tests. Green and red subscripts denote the performance changes relative to the Baseline and the Full Model , respectively.

Injected Topology (1/10)	Volume-W	SPIRE (Ours)	Gain ( $\Delta$ )
Star Graph	46.40	48.87	+2.47%
Degree-Rewired	46.43	49.90	+3.47%
Random ER	46.25	48.91	+2.66%

Table 6. Controlled stress test on Cora (

\text{Dirichlet }\beta=0.05,K=10

, 1 client corrupted) on global accuracy (%).

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Sep 5, 2026J/K move · Enter open · S save

Rethinking One-Shot Federated Graph Learning: Training-Free Statistical Estimation

Shutong Zheng, Sijia Chen

Sun Yat-sen University · The Hong Kong University of Science and Technology (Guangzhou)

Shrinkage Estimation Federated Graph Learning Non-IID Federated Learning Prototype Learning

Open paper AskPDF arXiv

One-shot federated graph learning generally aims to train Graph Neural Networks (GNNs) across clients with disconnected subgraphs in a single communication round. Existing methods predominantly design advanced optimization strategies under the premise that local GNN training is indispensable. However, empirical observations reveal that under extreme non-IID conditions, local GNN training suffers from severe cross-client representation misalignment, becoming a major source of error rather than a remedy. Motivated by this, we reformulate one-shot FGL as a statistical estimation problem. We propose SPEAR (Statistical Prototype Estimation with Adaptive Reliability), a completely training-free framework that directly computes topology-smoothed class prototypes from local graphs in the original feature space. The server then aggregates these prototypes using a sample-size-adaptive shrinkage estimator that down-weights unreliable local estimates, producing robust global class prototypes. Extensive experiments across seven benchmarks demonstrate that SPEAR consistently achieves state-of-the-art accuracy under extreme heterogeneity. Moreover, SPEAR delivers at least an order-of-magnitude speedup over all baselines, reaching several orders of magnitude against generative and distillation-based methods. Our findings suggest that training-free statistical estimation, rather than local GNN optimization, provides the key to robust and efficient one-shot federated graph learning. The code is available at https://github.com/Yodeesy/SPEAR .

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