Diffusion models have demonstrated effectiveness in generating natural images
and have been extended to generate diverse data types, including graphs. This
new generation of diffusion-based graph generative models has demonstrated
significant performance improvements over methods that rely on variational
autoencoders or generative adversarial networks. It's important to recognize,
however, that most of these models employ Gaussian or categorical diffusion
processes, which can struggle with sparse and long-tailed data distributions.
In our work, we introduce Graph Beta Diffusion (GBD), a diffusion-based
generative model particularly adept at capturing diverse graph structures. GBD
utilizes a beta diffusion process, tailored for the sparse and range-bounded
characteristics of graph adjacency matrices. Furthermore, we have developed a
modulation technique that enhances the realism of the generated graphs by
stabilizing the generation of critical graph structures, while preserving
flexibility elsewhere. The outstanding performance of GBD across three general
graph benchmarks and two biochemical graph benchmarks highlights its capability
to effectively capture the complexities of real-world graph data. The code will
be made available at this https URL

我们的研究引入了 Graph Beta Diffusion（GBD），一种特别擅长捕捉多样化图结构的扩散生成模型。GBD 利用了适用于图邻接矩阵的稀疏和有界特征的 Beta 扩散过程，并开发了调制技术来增强生成图的现实感，同时在其他地方保持灵活性。GBD 在三个通用图基准和两个生物化学图基准中的出色性能突显了其有效捕捉现实世界图数据复杂性的能力。

通过 Beta 扩散推进图生成

Advancing Graph Generation through Beta Diffusion

Diffusion-based graph generative models have recently obtained promising
results for graph generation. However, existing diffusion-based graph
generative models are mostly one-shot generative models that apply Gaussian
diffusion in the dequantized adjacency matrix space. Such a strategy can suffer
from difficulty in model training, slow sampling speed, and incapability of
incorporating constraints. We propose an \emph{autoregressive diffusion} model
for graph generation. Unlike existing methods, we define a node-absorbing
diffusion process that operates directly in the discrete graph space. For
forward diffusion, we design a \emph{diffusion ordering network}, which learns
a data-dependent node absorbing ordering from graph topology. For reverse
generation, we design a \emph{denoising network} that uses the reverse node
ordering to efficiently reconstruct the graph by predicting the node type of
the new node and its edges with previously denoised nodes at a time. Based on
the permutation invariance of graph, we show that the two networks can be
jointly trained by optimizing a simple lower bound of data likelihood. Our
experiments on six diverse generic graph datasets and two molecule datasets
show that our model achieves better or comparable generation performance with
previous state-of-the-art, and meanwhile enjoys fast generation speed.

我们提出了一种基于扩散的图生成模型，通过定义在离散图空间中操作的节点吸收扩散过程，设计了扩散排序网络和去噪网络，从而实现了更好或相当的生成性能，并且具有快速的生成速度。