Diffusion-based graph generative models have recently obtained promising results for graph generation. However, existing diffusion-based graph generative models are mostly 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 a data-dependent 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 the node type of the new node and its edges with previously denoised nodes at a time. Based on the permutation invariance of graph, we show that the two networks can be jointly trained by optimizing a simple lower bound of data likelihood. Our experiments on six diverse generic graph datasets and two molecule datasets show that our model achieves better or comparable generation performance with previous state-of-the-art, and meanwhile enjoys fast generation speed.

翻译：基于扩散的图生成模型近期在图生成任务中取得了令人瞩目的成果。然而，现有基于扩散的图生成模型多为一次性生成模型，这些模型在反量化邻接矩阵空间中应用高斯扩散。这种策略可能面临模型训练困难、采样速度慢以及难以融合约束条件等问题。为此，我们提出了一种面向图生成的*自回归扩散*模型。与现有方法不同，我们定义了一个直接作用于离散图空间的节点吸收扩散过程。在前向扩散中，我们设计了一个*扩散排序网络*，该网络能够从图拓扑中学习依赖数据的节点吸收排序。在反向生成过程中，我们设计了一个*去噪网络*，该网络利用反向节点排序，通过每次预测新节点的节点类型及其与先前已去噪节点的边，高效地重构整个图。基于图的排列不变性，我们证明这两个网络可以通过优化数据似然的一个简单下界进行联合训练。在六个通用图数据集和两个分子数据集上的实验表明，我们的模型在取得与先前最先进方法相当或更优生成性能的同时，还具备快速的生成速度。