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

arXiv: https://arxiv.org/abs/2508.14351 · HTML: https://mlsanity.com/paper/2508.14351/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 74 references that are in the map.
- First posted on arXiv 20 Aug 2025.

## Builds on (most cited first, 30 of 50)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018)
- [Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions](https://mlsanity.com/paper/2211.01916/) (2022)
- [MoFlow: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/2006.10137/) (2020)
- [Convergence of score-based generative modeling for general data distributions](https://mlsanity.com/paper/2209.12381/) (2022)
- [Convergence for score-based generative modeling with polynomial complexity](https://mlsanity.com/paper/2206.06227/) (2022)
- [Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data](https://mlsanity.com/paper/2302.07194/) (2023)
- [The probability flow ODE is provably fast](https://mlsanity.com/paper/2305.11798/) (2023)
- [Contextual Stochastic Block Models](https://mlsanity.com/paper/1807.09596/) (2018)
- [MARS: Markov Molecular Sampling for Multi-objective Drug Discovery](https://mlsanity.com/paper/2103.10432/) (2021)

## Built on by (most cited first, 3 of 3)

- [Structuring Semantic Embeddings for Principle Evaluation: A Prototype-Guided Contrastive Learning Approach](https://mlsanity.com/paper/2608.15224/) (2026)
- [Structuring Relations Among Learning Paradigms via Protocol--Objective--Resource Reductions](https://mlsanity.com/paper/2609.32766/) (2026)
- [Graph Representation via Elements of Discrete Morse and Cobordism Theories](https://mlsanity.com/paper/2610.01937/) (2026)

## Abstract (arXiv)

Score-based graph generative models (SGGMs) have proven effective in critical applications such as drug discovery and protein synthesis. However, their theoretical behavior, particularly regarding convergence, remains underexplored. Unlike common score-based generative models (SGMs), which are governed by a single stochastic differential equation (SDE), SGGMs involve a system of coupled SDEs. In SGGMs, the graph structure and node features are governed by separate but interdependent SDEs. This distinction makes existing convergence analyses from SGMs inapplicable for SGGMs. In this work, we present the first non-asymptotic 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 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 synthetic graph models, and the results align with our theoretical predictions. This work deepens the theoretical understanding of SGGMs, demonstrates their applicability in critical domains, and provides practical guidance for designing effective models.