Graph Generation with Diffusion Mixture

TL;DR

This paper introduces a novel diffusion-based graph generation framework that explicitly models graph topology through a mixture of endpoint-conditioned diffusion processes, leading to improved generation of structurally accurate graphs.

Contribution

It proposes a new generative framework that explicitly learns graph structures using a mixture of diffusion processes, enabling better topology modeling and maximum likelihood training.

Findings

Outperforms previous models in graph generation tasks.

Generates graphs with correct topology for both continuous and discrete features.

Effective on general graphs and molecular structures.

Abstract

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.