Towards understanding Diffusion Models (on Graphs)

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? Our findings aim to enhance the understanding of diffusion models and in the long run their application in graph machine learning. The forward process is modelled by a Markov process. The reverse process is unknown and needs to be approximated; this is usually done with a neural network. Consider the analogy of dropping a small amount of paint into a glass of water. Initially, the paint is concentrated in one location, but over time, it diffuses throughout the water until it reaches a state of equilibrium.