Autoregressive Diffusion Model for Graph Generation

Lingkai Kong, Jiaming Cui, Haotian Sun, Yuchen Zhuang, B. Aditya Prakash, Chao Zhang

Keywords: graph generation, diffusion based generative model

TL;DR: A new autoregressive diffusion model for graph generation

Abstract: Diffusion-based graph generative models have recently obtained promising results for graph generation. However, existing diffusion-based graph generative models are all one-shot generative models that apply Gaussian diffusion in the dequantized adjacency matrix space. Such a strategy can suffer from difficulty in model training, slow sampling speed, and incapability of incorporating constraints. We propose an \emph{autoregressive diffusion} model for graph generation. Unlike existing methods, we define a node-absorbing diffusion process that operates directly in the discrete graph space. For forward diffusion, we design a \emph{diffusion ordering network}, which learns an optimal node absorbing ordering from graph topology. For reverse generation, we design a \emph{denoising network} that uses the reverse node ordering to efficiently reconstruct the graph by predicting one row of the adjacency matrix at a time. Based on permutation invariance of graph generation, we show that the two networks can be jointly trained by optimizing a simple lower bound of data likelihood. Our experiments on six diverse datasets show that our model achieves better or comparable generation performance with previous state-of-the-art, and meanwhile enjoys fast generation speed.

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