AI 中文总结
提出一种离散图扩散模型，通过结构候选限制降低训练复杂度，并采用度感知下限余弦噪声调度，实现大规模图的高保真生成。
AI 中文摘要
当感兴趣的图规模较大且真实世界样本有限或访问敏感时，在规模上合成逼真的图至关重要。基于扩散的生成器近期推动了大部分进展，提供了高建模能力，但大多数此类方法具有二次计算复杂度，因此仅限于小规模网络，目前最多支持3k节点。现有的非二次方法仍受记忆问题以及可扩展性与生成质量之间权衡的限制。我们的目标是生成大规模图，其结构统计——例如度分布、聚类系数和路径长度——忠实反映真实世界稀疏图的特征，而不诉诸于记忆训练数据。我们引入了一种离散图扩散模型，将训练限制在结构上合理的节点对子集——观察到的边及其楔形非边——从而将训练复杂度降低到节点数的二次以下。为了在整个前向和反向轨迹中保持噪声图的信息量，我们设计了一个由度感知、下限余弦噪声调度控制的三类吸收前向过程：与对每对节点同等地添加噪声的结构盲调度不同，我们的调度适应每个节点的度，并且永远不会完全抹去图的结构，从而在每一步保持噪声图的信息量。跨多个数据集的实验表明，在大型图生成中，我们的模型在结构保真度方面始终位列现有离散扩散基线的前列。
英文摘要
Synthesizing realistic graphs at scale is vital when the graphs of interest are large and real-world samples are limited or access-sensitive. Diffusion-based generators have recently driven much of the progress, offering high modeling capacity, but most such methods have quadratic computational complexity and are hence restricted to small-scale networks, currently up to 3k nodes. Existing non-quadratic methods remain limited by memorization issues and a trade-off between scalability and generation quality. Our goal is to generate large graphs whose structural statistics --- e.g., degree distribution, clustering, and path length --- faithfully reflect those of real-world sparse graphs, without resorting to memorizing the training data. We introduce a discrete graph diffusion model that restricts training to a structurally motivated subset of node pairs --- observed edges and their wedge non-edges --- reducing training complexity below quadratic in the number of nodes. To keep the noisy graph informative throughout both the forward and reverse trajectories, we design a three-class absorbing forward process governed by a \emph{degree-aware, floored} cosine noise schedule: unlike a structure-blind schedule that adds noise to every pair identically, ours adapts to each node's degree and never fully erases the graph's structure, keeping the noisy graph informative at every step. Experiments across diverse datasets show that our model consistently ranks among the top methods for structural fidelity against existing discrete diffusion baselines in large graph generation.
