Graph diffusion models achieve state-of-the-art performance in graph generation but suffer from quadratic complexity in the number of nodes -- and much of their capacity is wasted modeling the absence of edges in sparse graphs. Inspired by latent diffusion in other modalities, a natural idea is to compress graphs into a low-dimensional latent space and perform diffusion there. However, unlike images or text, graph generation requires nearly lossless reconstruction, as even a single error in decoding an adjacency matrix can render the entire sample invalid. This challenge has remained largely unaddressed. We propose LG-Flow, a latent graph diffusion framework that directly overcomes these obstacles. A permutation-equivariant autoencoder maps each node into a fixed-dimensional embedding from which the full adjacency is provably recoverable, enabling near-lossless reconstruction for both undirected graphs and DAGs. The dimensionality of this latent representation scales linearly with the number of nodes, eliminating the quadratic bottleneck and making it feasible to train larger and more expressive models. In this latent space, we train a Diffusion Transformer with flow matching, enabling efficient and expressive graph generation. Our approach achieves competitive results against state-of-the-art graph diffusion models, while achieving up to $1000\times$ speed-up. Our code is available at https://github.com/asiraudin/LG-Flow .

翻译：图扩散模型在图生成任务中取得了最先进的性能，但存在节点数量二次方复杂度的问题——其大部分建模能力被浪费在稀疏图中不存在的边上。受其他模态中潜在扩散的启发，一个自然的想法是将图压缩到低维潜在空间并在其中进行扩散。然而，与图像或文本不同，图生成需要近乎无损的重建，因为即使邻接矩阵解码中出现单个错误，也可能导致整个样本无效。这一挑战在很大程度上仍未得到解决。我们提出了LG-Flow，一个直接克服这些障碍的潜在图扩散框架。一个置换等变自编码器将每个节点映射到固定维度的嵌入中，从该嵌入中可以理论上完全恢复完整的邻接矩阵，从而为无向图和有向无环图实现近乎无损的重建。该潜在表示的维度与节点数量呈线性关系，消除了二次方瓶颈，使得训练更大、更具表达力的模型成为可能。在此潜在空间中，我们训练了一个基于流匹配的扩散Transformer，实现了高效且富有表现力的图生成。我们的方法在与最先进的图扩散模型对比中取得了具有竞争力的结果，同时实现了高达$1000\times$的加速。我们的代码可在https://github.com/asiraudin/LG-Flow获取。