Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. Although diffusion models have achieved notable success in graph generation recently, they are ill-suited for modeling the topological properties of graphs since learning to denoise the noisy samples does not explicitly learn the graph structures to be generated. To tackle this limitation, we propose a generative framework that models the topology of graphs by explicitly learning the final graph structures of the diffusion process. Specifically, we design the generative process as a mixture of endpoint-conditioned diffusion processes which is driven toward the predicted graph that results in rapid convergence. We further introduce a simple parameterization of the mixture process and develop an objective for learning the final graph structure, which enables maximum likelihood training. Through extensive experimental validation on general graph and 2D/3D molecule generation tasks, we show that our method outperforms previous generative models, generating graphs with correct topology with both continuous (e.g. 3D coordinates) and discrete (e.g. atom types) features. Our code is available at https://github.com/harryjo97/GruM.
Diffusion Model Conditioning on Gaussian Mixture Model and Negative Gaussian Mixture Gradient
University of Macau（澳门大学）；Great Bay University（大湾区大学）；Great Bay Institute for Advanced Study（大湾区高等研究院）；University of Science and Technology of China（中国科学技术大学）
Universality of Gaussian-Mixture Reverse Kernels in Conditional Diffusion
Center for Mathematics and Interdisciplinary Sciences, Fudan University（复旦大学数学与交叉科学中心）；Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS)（上海数学与交叉科学研究院（SIMIS））；Northeastern University（东北大学）；Infectious Diseases Division, icddr,b（icddr,b传染病部门）；Rutgers University（罗格斯大学）
Unraveling the Smoothness Properties of Diffusion Models: A Gaussian Mixture Perspective
The University of Hong Kong（香港大学）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；The Simons Institute for the Theory of Computing at the University of California, Berkeley（加州大学伯克利分校西蒙斯理论计算研究所）；University of Pennsylvania（宾夕法尼亚大学）
Beijing Key Laboratory of Big Data Management and Analysis Methods（大数据管理与分析方法北京市重点实验室）；Tsinghua University（清华大学）；Sea AI Lab；Gaoling School of Artificial Intelligence, Renmin University of China（中国人民大学高瓴人工智能学院）
MIXGAN: Learning Concepts from Different Domains for Mixture Generation
Sun Yat-sen University（中山大学）；Guangdong Key Laboratory of Big Data Analysis and Processing（广东省大数据分析与处理重点实验室）；Key Laboratory of Machine Intelligence and Advanced Computing, Ministry of Education（机器智能与先进计算教育部重点实验室）；NUDT（国防科技大学）
Go With the Flow: Fast Diffusion for Gaussian Mixture Models
Georgia Institute of Technology（佐治亚理工学院）；University of Oklahoma（俄克拉荷马大学）；FAMU-FSU College of Engineering（佛罗里达大学-佛罗里达州立大学工程学院）；Florida State University（佛罗里达州立大学）
Unlocking Cross-Scenario Physical Layer Security: A Mixture-of-Experts Framework with Generative Diffusion Models
Shenzhen Research Institute of Northwestern Polytechnical University（西北工业大学深圳研究院）；Northwestern Polytechnical University（西北工业大学）；Pengcheng Laboratory（鹏城实验室）；University of Houston（休斯顿大学）
