# Advancing Graph Generation through Beta Diffusion arXiv: https://arxiv.org/abs/2406.09357 ยท HTML: https://mlsanity.com/paper/2406.09357/ ## Key facts - Cited by 13 papers in the map (data through 14 Oct 2026). - Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. - Builds on 46 of its 68 references that are in the map. - First posted on arXiv 13 Jun 2024. ## Placed in - Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/) ## Builds on (most cited first, 30 of 46) - [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020) - [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019) - [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) - [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022) - [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017) - [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021) - [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016) - [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) - [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022) - [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018) - [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) - [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017) - [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020) - [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) - [Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Models](https://mlsanity.com/paper/2305.18455/) (2023) - [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018) - [Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generation](https://mlsanity.com/paper/2404.04057/) (2024) - [Constrained Graph Variational Autoencoders for Molecule Design](https://mlsanity.com/paper/1805.09076/) (2018) - [MoFlow: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/2006.10137/) (2020) - [GraphDF: A Discrete Flow Model for Molecular Graph Generation](https://mlsanity.com/paper/2102.01189/) (2021) - [GraphGAN: Graph Representation Learning with Generative Adversarial Nets](https://mlsanity.com/paper/1711.08267/) (2017) - [Graph Normalizing Flows](https://mlsanity.com/paper/1905.13177/) (2019) - [SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators](https://mlsanity.com/paper/2204.01613/) (2022) - [Autoregressive Diffusion Model for Graph Generation](https://mlsanity.com/paper/2307.08849/) (2023) - [Molecular graph generation with Graph Neural Networks](https://mlsanity.com/paper/2012.07397/) (2020) ## Built on by (most cited first, 13 of 13) - [PowerGrow: Feasible Co-Growth of Structures and Dynamics for Power Grid Synthesis](https://mlsanity.com/paper/2509.12212/) (2025) - [Graph-GRPO: Training Graph Flow Models with Reinforcement Learning](https://mlsanity.com/paper/2603.10395/) (2026) - [Flowette: Flow Matching with Graphette Priors for Graph Generation](https://mlsanity.com/paper/2602.23566/) (2026) - [Detecting and Mitigating Memorization in Diffusion Models through Anisotropy of the Log-Probability](https://mlsanity.com/paper/2601.20642/) (2026) - [Unrestrained Simplex Denoising for Discrete Data. A Non-Markovian Approach Applied to Graph Generation](https://mlsanity.com/paper/2603.28572/) (2026) - [Hierarchical Discrete Flow Matching for Graph Generation](https://mlsanity.com/paper/2604.00236/) (2026) - [Designing ReLU Generative Networks to Enumerate Trees with a Given Tree Edit Distance](https://mlsanity.com/paper/2510.10706/) (2025) - [Is Noise Conditioning Necessary? A Unified Theory of Unconditional Graph Diffusion Models](https://mlsanity.com/paper/2505.22935/) (2025) - [A Systematic Evaluation of Co-folding Model Representations for Small-Molecule Learning](https://mlsanity.com/paper/2602.13249/) (2026) - [ReLU Networks for Exact Generation of Similar Graphs](https://mlsanity.com/paper/2604.05929/) (2026) - [Operationally Feasible Synthetic Power-Grid Scenarios via Learning the AC-Operable Joint Distribution](https://mlsanity.com/paper/2608.03878/) (2026) - [GeoGAE: Scalable Graph-Level Autoencoding via Hyperball Cloud Representations](https://mlsanity.com/paper/2609.35527/) (2026) - [Stable Transformers for Graph Generation](https://mlsanity.com/paper/2609.39739/) (2026) ## Abstract (arXiv) Diffusion models have excelled in generating natural images and are now being adapted to a variety of data types, including graphs. However, conventional models often rely on Gaussian or categorical diffusion processes, which can struggle to accommodate the mixed discrete and continuous components characteristic of graph data. Graphs typically feature discrete structures and continuous node attributes that often exhibit rich statistical patterns, including sparsity, bounded ranges, skewed distributions, and long-tailed behavior. To address these challenges, we introduce Graph Beta Diffusion (GBD), a generative model specifically designed to handle the diverse nature of graph data. GBD leverages a beta diffusion process, effectively modeling both continuous and discrete elements. Additionally, we propose a modulation technique that enhances the realism of generated graphs by stabilizing critical graph topology while maintaining flexibility for other components. GBD competes strongly with existing models across multiple general and biochemical graph benchmarks, showcasing its ability to capture the intricate balance between discrete and continuous features inherent in real-world graph data. The PyTorch code is available on GitHub.