Graph generative models often face a critical trade-off between learning complex distributions and achieving fast generation speed. We introduce Autoregressive Noisy Filtration Modeling (ANFM), a novel approach that addresses both challenges. ANFM leverages filtration, a concept from topological data analysis, to transform graphs into short sequences of monotonically increasing subgraphs. This formulation extends the sequence families used in previous autoregressive models. To learn from these sequences, we propose a novel autoregressive graph mixer model. Our experiments suggest that exposure bias might represent a substantial hurdle in autoregressive graph generation and we introduce two mitigation strategies to address it: noise augmentation and a reinforcement learning approach. Incorporating these techniques leads to substantial performance gains, making ANFM competitive with state-of-the-art diffusion models across diverse synthetic and real-world datasets. Notably, ANFM produces remarkably short sequences, achieving a 100-fold speedup in generation time compared to diffusion models. This work marks a significant step toward high-throughput graph generation.

翻译：图生成模型常常面临学习复杂分布与实现快速生成速度之间的关键权衡。本文提出自动回归噪声过滤建模（ANFM），一种同时应对这两项挑战的新方法。ANFM利用来自拓扑数据分析的过滤概念，将图转化为单调递增子图的短序列。该公式扩展了先前自回归模型所使用的序列族。为了从这些序列中学习，我们提出了一种新颖的自回归图混合器模型。我们的实验表明，暴露偏差可能是自回归图生成中的一个重大障碍，并引入了两种缓解策略：噪声增强和强化学习方法。结合这些技术带来了显著的性能提升，使得ANFM在多种合成和真实世界数据集上与最先进的扩散模型相竞争。值得注意的是，ANFM生成的序列非常短，与扩散模型相比实现了100倍的生成时间加速。这项工作标志着向高通量图生成迈出了重要一步。