# Understanding and contextualising diffusion models

arXiv: https://arxiv.org/abs/2302.01394 · HTML: https://mlsanity.com/paper/2302.01394/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 15 of its 20 references that are in the map.
- First posted on arXiv 26 Jan 2023.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 15 of 15)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (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)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Optimizing Prompts for Text-to-Image Generation](https://mlsanity.com/paper/2212.09611/) (2022)
- [Non Gaussian Denoising Diffusion Models](https://mlsanity.com/paper/2106.07582/) (2021)
- [Bilateral Denoising Diffusion Models](https://mlsanity.com/paper/2108.11514/) (2021)
- [Image Modeling with Deep Convolutional Gaussian Mixture Models](https://mlsanity.com/paper/2104.12686/) (2021)

## Built on by (most cited first, 1 of 1)

- [Training Implicit Generative Models via an Invariant Statistical Loss](https://mlsanity.com/paper/2402.16435/) (2024)

## Abstract (arXiv)

The latest developments in Artificial Intelligence include diffusion generative models, quite popular tools which can produce original images both unconditionally and, in some cases, conditioned by some inputs provided by the user. Apart from implementation details, which are outside the scope of this work, all of the main models used to generate images are substantially based on a common theory which restores a new image from a completely degraded one. In this work we explain how this is possible by focusing on the mathematical theory behind them, i.e. without analyzing in detail the specific implementations and related methods. The aim of this work is to clarify to the interested reader what all this means mathematically and intuitively.