Diffusion models based on permutation-equivariant networks can learn permutation-invariant distributions for graph data. However, in comparison to their non-invariant counterparts, we have found that these invariant models encounter greater learning challenges since 1) their effective target distributions exhibit more modes; 2) their optimal one-step denoising scores are the score functions of Gaussian mixtures with more components. Motivated by this analysis, we propose a non-invariant diffusion model, called $\textit{SwinGNN}$, which employs an efficient edge-to-edge 2-WL message passing network and utilizes shifted window based self-attention inspired by SwinTransformers. Further, through systematic ablations, we identify several critical training and sampling techniques that significantly improve the sample quality of graph generation. At last, we introduce a simple post-processing trick, $\textit{i.e.}$, randomly permuting the generated graphs, which provably converts any graph generative model to a permutation-invariant one. Extensive experiments on synthetic and real-world protein and molecule datasets show that our SwinGNN achieves state-of-the-art performances. Our code is released at https://github.com/qiyan98/SwinGNN.

翻译：基于置换等变网络的扩散模型能够学习图数据的置换不变分布。然而，与非不变对应模型相比，我们发现在这些不变模型面临更大的学习挑战，原因在于：1）它们的有效目标分布具有更多模态；2）其最优一步去噪分数是含有更多分量的高斯混合模型的分数函数。受此分析启发，我们提出一种非不变扩散模型——SwinGNN，该模型采用高效的边到边2-WL消息传递网络，并利用受SwinTransformer启发的基于滑动窗口的自注意力机制。此外，通过系统性消融实验，我们识别出若干关键训练与采样技术，可显著提升图生成样本质量。最后，我们引入一种简单的后处理技巧——即对生成图进行随机置换，可被证明将任何图生成模型转换为置换不变模型。在合成数据集及真实蛋白质与分子数据集上的大量实验表明，我们的SwinGNN实现了最先进的性能。我们的代码已发布于 https://github.com/qiyan98/SwinGNN。