Graph generation has been dominated by autoregressive models due to their simplicity and effectiveness, despite their sensitivity to ordering. Yet diffusion models have garnered increasing attention, as they offer comparable performance while being permutation-invariant. Current graph diffusion models generate graphs in a one-shot fashion, but they require extra features and thousands of denoising steps to achieve optimal performance. We introduce PARD, a Permutation-invariant Auto Regressive Diffusion model that integrates diffusion models with autoregressive methods. PARD harnesses the effectiveness and efficiency of the autoregressive model while maintaining permutation invariance without ordering sensitivity. Specifically, we show that contrary to sets, elements in a graph are not entirely unordered and there is a unique partial order for nodes and edges. With this partial order, PARD generates a graph in a block-by-block, autoregressive fashion, where each block's probability is conditionally modeled by a shared diffusion model with an equivariant network. To ensure efficiency while being expressive, we further propose a higher-order graph transformer, which integrates transformer with PPGN. Like GPT, we extend the higher-order graph transformer to support parallel training of all blocks. Without any extra features, PARD achieves state-of-the-art performance on molecular and non-molecular datasets, and scales to large datasets like MOSES containing 1.9M molecules. Pard is open-sourced at https://github.com/LingxiaoShawn/Pard.

翻译：图生成领域长期由自回归模型主导，尽管其对排序敏感，但因其简单性和有效性而被广泛采用。然而，扩散模型因其在保持置换不变性的同时提供可比性能而日益受到关注。当前的图扩散模型以单次生成方式产生图，但需要额外特征和数千步去噪过程才能达到最优性能。本文提出PARD，一种置换不变自回归扩散模型，将扩散模型与自回归方法相结合。PARD既保持了自回归模型的有效性和效率，又维持了置换不变性而无排序敏感性。具体而言，我们证明与集合不同，图中的元素并非完全无序，节点和边存在唯一的偏序关系。基于此偏序，PARD以分块自回归方式生成图，其中每个块的概率由具有等变网络的共享扩散模型进行条件建模。为确保高效性与表达力，我们进一步提出高阶图Transformer，将Transformer与PPGN相结合。借鉴GPT的思想，我们扩展高阶图Transformer以支持所有块的并行训练。在无需任何额外特征的情况下，PARD在分子和非分子数据集上实现了最先进的性能，并可扩展至包含190万个分子的大型数据集MOSES。Pard已在https://github.com/LingxiaoShawn/Pard开源。