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

Traditional model-based diagnosis relies on constructing explicit system
models, a process that can be laborious and expertise-demanding. In this paper,
we propose a novel framework that combines concepts of model-based diagnosis
with deep graph structure learning. This data-driven approach leverages data to
learn the system's underlying structure and provide dynamic observations,
represented by two distinct graph adjacency matrices. Our work facilitates a
seamless integration of graph structure learning with model-based diagnosis by
making three main contributions: (i) redefining the constructs of system
representation, observations, and faults (ii) introducing two distinct versions
of a self-supervised graph structure learning model architecture and (iii)
demonstrating the potential of our data-driven diagnostic method through
experiments on a system of coupled oscillators.

本文提出了一种新颖的框架，将基于模型的诊断与深度图结构学习的概念相结合。通过利用数据学习系统的底层结构和提供动态观察，该方法实现了图结构学习与基于模型的诊断的无缝集成，并通过在耦合振荡器系统上的实验证明了其数据驱动诊断方法的潜力。

图结构残差：一种学习诊断方法

Graph Structural Residuals: A Learning Approach to Diagnosis

We study lower bounds for the problem of approximating a one dimensional
distribution given (noisy) measurements of its moments. We show that there are
distributions on $[-1,1]$ that cannot be approximated to accuracy $\epsilon$ in
Wasserstein-1 distance even if we know \emph{all} of their moments to
multiplicative accuracy $(1\pm2^{-\Omega(1/\epsilon)})$; this result matches an
upper bound of Kong and Valiant [Annals of Statistics, 2017]. To obtain our
result, we provide a hard instance involving distributions induced by the
eigenvalue spectra of carefully constructed graph adjacency matrices.
Efficiently approximating such spectra in Wasserstein-1 distance is a
well-studied algorithmic problem, and a recent result of Cohen-Steiner et al.
[KDD 2018] gives a method based on accurately approximating spectral moments
using $2^{O(1/\epsilon)}$ random walks initiated at uniformly random nodes in
the graph.
As a strengthening of our main result, we show that improving the dependence
on $1/\epsilon$ in this result would require a new algorithmic approach.
Specifically, no algorithm can compute an $\epsilon$-accurate approximation to
the spectrum of a normalized graph adjacency matrix with constant probability,
even when given the transcript of $2^{\Omega(1/\epsilon)}$ random walks of
length $2^{\Omega(1/\epsilon)}$ started at random nodes.

研究通过给出（有噪声的）矩的测量值来近似一维分布的问题的下限。