Understanding and contextualising diffusion models

TL;DR

This paper explains the mathematical foundations of diffusion generative models, clarifying how they restore images from degraded versions, to help readers understand their core principles without focusing on implementation details.

Contribution

It provides a clear, theory-based explanation of diffusion models' mathematical principles, enhancing understanding of their image generation process.

Findings

Diffusion models are based on restoring images from degraded versions.

The paper clarifies the mathematical intuition behind diffusion processes.

It helps demystify the core concepts of diffusion-based image generation.

Abstract

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.