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 structural information of graphs since learning to denoise the noisy samples does not explicitly capture the graph topology. To tackle this limitation, we propose a novel generative process that models the topology of graphs by predicting the destination of the process. Specifically, we design the generative process as a mixture of diffusion processes conditioned on the endpoint in the data distribution, which drives the process toward the probable destination. Further, we introduce new training objectives for learning to predict the destination, and discuss the advantages of our generative framework that can explicitly model the graph topology and exploit the inductive bias of the data. Through extensive experimental validation on general graph and 2D/3D molecular graph generation tasks, we show that our method outperforms previous generative models, generating graphs with correct topology with both continuous and discrete features.

翻译：图的生成对于需要理解其非欧几里得结构复杂性的现实世界任务而言是一项重大挑战。尽管扩散模型近期在图生成领域取得了显著成功，但由于学习去噪样本的过程并未显式捕捉图的拓扑结构，因此它们不适合建模图的结构信息。为应对这一局限性，我们提出了一种新颖的生成过程，通过预测该过程的目的地来建模图的拓扑结构。具体而言，我们将生成过程设计为以数据分布中的端点为条件的扩散过程混合，从而驱动生成过程朝向可能的目的地。此外，我们引入了用于学习预测目的地的新训练目标，并讨论了我们的生成框架的优势，该框架能够显式建模图的拓扑结构并利用数据的归纳偏置。通过在通用图生成任务以及二维/三维分子图生成任务上的广泛实验验证，我们表明，我们的方法优于先前的生成模型，能够生成具有正确拓扑结构且兼具连续与离散特征的图。