# Towards understanding Diffusion Models (on Graphs)

arXiv: https://arxiv.org/abs/2409.00374 · HTML: https://mlsanity.com/paper/2409.00374/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 11 of its 11 references that are in the map.
- First posted on arXiv 31 Aug 2024.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 11 of 11)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Score-based Diffusion Models in Function Space](https://mlsanity.com/paper/2302.07400/) (2023)
- [Diffusion Models for Graphs Benefit From Discrete State Spaces](https://mlsanity.com/paper/2210.01549/) (2022)
- [Sampling, Diffusions, and Stochastic Localization](https://mlsanity.com/paper/2305.10690/) (2023)

## Abstract (arXiv)

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.