标题： 理解扩散模型（在图上的） 显示英文标题

标题： Towards understanding Diffusion Models (on Graphs)

摘要： 扩散模型从各种理论和方法论的角度出现，每个角度都为其基本原理提供了独特的见解。 在这项工作中，我们概述了最突出的方法，并注意到了它们惊人的类比——即看似不同的方法如何收敛到核心问题的相似数学公式。 虽然我们的最终目标是在图的背景下理解这些模型，但我们首先在一个更简单的环境中进行实验以建立基础见解。 通过不同扩散和采样技术的经验性研究，我们探讨了三个关键问题：（1）噪声在这些模型中扮演什么角色？（2）采样方法的选择对结果的影响有多大？（3）神经网络正在逼近什么函数，最优性能是否需要高复杂度？ 我们的发现旨在增强对扩散模型的理解，并长远来看增强其在图机器学习中的应用。 显示英文摘要

摘要： Diffusion models have emerged from various theoretical and methodological perspectives, each offering unique insights into their underlying principles. In this work, we provide an overview of the most prominent approaches, drawing attention to their striking analogies -- namely, how seemingly diverse methodologies converge to a similar mathematical formulation of the core problem. While our ultimate goal is to understand these models in the context of graphs, we begin by conducting experiments in a simpler setting to build foundational insights. Through an empirical investigation of different diffusion and sampling techniques, we explore three critical questions: (1) What role does noise play in these models? (2) How significantly does the choice of the sampling method affect outcomes? (3) What function is the neural network approximating, and is high complexity necessary for optimal performance? Our findings aim to enhance the understanding of diffusion models and in the long run their application in graph machine learning.