Generalised Diffusion Probabilistic Scale-Spaces

TL;DR

This paper introduces a generalized scale-space theory for diffusion probabilistic models, linking them to classical image filtering techniques like diffusion and osmosis filters, and explores their theoretical foundations.

Contribution

It develops a unified theoretical framework connecting diffusion probabilistic models with classical image filtering, enhancing understanding of their underlying principles.

Findings

Establishes connections between diffusion models and classical filters

Provides a theoretical basis for diffusion probabilistic models

Shows empirical links to diffusion and osmosis filters

Abstract

Diffusion probabilistic models excel at sampling new images from learned distributions. Originally motivated by drift-diffusion concepts from physics, they apply image perturbations such as noise and blur in a forward process that results in a tractable probability distribution. A corresponding learned reverse process generates images and can be conditioned on side information, which leads to a wide variety of practical applications. Most of the research focus currently lies on practice-oriented extensions. In contrast, the theoretical background remains largely unexplored, in particular the relations to drift-diffusion. In order to shed light on these connections to classical image filtering, we propose a generalised scale-space theory for diffusion probabilistic models. Moreover, we show conceptual and empirical connections to diffusion and osmosis filters.