# Generalised Scale-Space Properties for Probabilistic Diffusion Models

arXiv: https://arxiv.org/abs/2303.07900 · HTML: https://mlsanity.com/paper/2303.07900/

## 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 8 of its 35 references that are in the map.
- First posted on arXiv 14 Mar 2023.

## Placed in

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

## Builds on (most cited first, 8 of 8)

- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Generalized Normalizing Flows via Markov Chains](https://mlsanity.com/paper/2111.12506/) (2021)
- [The circular SiZer, inferred persistence of shape parameters and application to early stem cell differentiation](https://mlsanity.com/paper/1404.3300/) (2014)
- [Variational Osmosis for Non-linear Image Fusion](https://mlsanity.com/paper/1910.02012/) (2019)

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

- [Generalised Diffusion Probabilistic Scale-Spaces](https://mlsanity.com/paper/2309.08511/) (2023)

## Abstract (arXiv)

Probabilistic diffusion models enjoy increasing popularity in the deep learning community. They generate convincing samples from a learned distribution of input images with a wide field of practical applications. Originally, these approaches were motivated from drift-diffusion processes, but these origins find less attention in recent, practice-oriented publications. We investigate probabilistic diffusion models from the viewpoint of scale-space research and show that they fulfil generalised scale-space properties on evolving probability distributions. Moreover, we discuss similarities and differences between interpretations of the physical core concept of drift-diffusion in the deep learning and model-based world. To this end, we examine relations of probabilistic diffusion to osmosis filters.