A Non-Asymptotic Convergent Analysis for Scored-Based Graph Generative Model via a System of Stochastic Differential Equations

Junwei Su, Chuan Wu
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:57046-57083, 2025.

Abstract

This paper investigates the convergence behavior of score-based graph generative models (SGGMs). Unlike common score-based generative models (SGMs) that are governed by a single stochastic differential equation (SDE), SGGMs utilize a system of dependent SDEs, where the graph structure and node features are modeled separately, while accounting for their inherent dependencies. This distinction makes existing convergence analyses from SGMs inapplicable for SGGMs. In this work, we present the first convergence analysis for SGGMs, focusing on the convergence bound (the risk of generative error) across three key graph generation paradigms: (1) feature generation with a fixed graph structure, (2) graph structure generation with fixed node features, and (3) joint generation of both graph structure and node features. Our analysis reveals several unique factors specific to SGGMs (e.g., the topological properties of the graph structure) which significantly affect the convergence bound. Additionally, we offer theoretical insights into the selection of hyperparameters (e.g., sampling steps and diffusion length) and advocate for techniques like normalization to improve convergence. To validate our theoretical findings, we conduct a controlled empirical study using a synthetic graph model. The results in this paper contribute to a deeper theoretical understanding of SGGMs and offer practical guidance for designing more efficient and effective SGGMs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-su25c, title = {A Non-Asymptotic Convergent Analysis for Scored-Based Graph Generative Model via a System of Stochastic Differential Equations}, author = {Su, Junwei and Wu, Chuan}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {57046--57083}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/su25c/su25c.pdf}, url = {https://proceedings.mlr.press/v267/su25c.html}, abstract = {This paper investigates the convergence behavior of score-based graph generative models (SGGMs). Unlike common score-based generative models (SGMs) that are governed by a single stochastic differential equation (SDE), SGGMs utilize a system of dependent SDEs, where the graph structure and node features are modeled separately, while accounting for their inherent dependencies. This distinction makes existing convergence analyses from SGMs inapplicable for SGGMs. In this work, we present the first convergence analysis for SGGMs, focusing on the convergence bound (the risk of generative error) across three key graph generation paradigms: (1) feature generation with a fixed graph structure, (2) graph structure generation with fixed node features, and (3) joint generation of both graph structure and node features. Our analysis reveals several unique factors specific to SGGMs (e.g., the topological properties of the graph structure) which significantly affect the convergence bound. Additionally, we offer theoretical insights into the selection of hyperparameters (e.g., sampling steps and diffusion length) and advocate for techniques like normalization to improve convergence. To validate our theoretical findings, we conduct a controlled empirical study using a synthetic graph model. The results in this paper contribute to a deeper theoretical understanding of SGGMs and offer practical guidance for designing more efficient and effective SGGMs.} }
Endnote
%0 Conference Paper %T A Non-Asymptotic Convergent Analysis for Scored-Based Graph Generative Model via a System of Stochastic Differential Equations %A Junwei Su %A Chuan Wu %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-su25c %I PMLR %P 57046--57083 %U https://proceedings.mlr.press/v267/su25c.html %V 267 %X This paper investigates the convergence behavior of score-based graph generative models (SGGMs). Unlike common score-based generative models (SGMs) that are governed by a single stochastic differential equation (SDE), SGGMs utilize a system of dependent SDEs, where the graph structure and node features are modeled separately, while accounting for their inherent dependencies. This distinction makes existing convergence analyses from SGMs inapplicable for SGGMs. In this work, we present the first convergence analysis for SGGMs, focusing on the convergence bound (the risk of generative error) across three key graph generation paradigms: (1) feature generation with a fixed graph structure, (2) graph structure generation with fixed node features, and (3) joint generation of both graph structure and node features. Our analysis reveals several unique factors specific to SGGMs (e.g., the topological properties of the graph structure) which significantly affect the convergence bound. Additionally, we offer theoretical insights into the selection of hyperparameters (e.g., sampling steps and diffusion length) and advocate for techniques like normalization to improve convergence. To validate our theoretical findings, we conduct a controlled empirical study using a synthetic graph model. The results in this paper contribute to a deeper theoretical understanding of SGGMs and offer practical guidance for designing more efficient and effective SGGMs.
APA
Su, J. & Wu, C.. (2025). A Non-Asymptotic Convergent Analysis for Scored-Based Graph Generative Model via a System of Stochastic Differential Equations. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:57046-57083 Available from https://proceedings.mlr.press/v267/su25c.html.

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