# Generalised Diffusion Probabilistic Scale-Spaces

arXiv: https://arxiv.org/abs/2309.08511 · HTML: https://mlsanity.com/paper/2309.08511/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 27 of its 83 references that are in the map.
- First posted on arXiv 15 Sep 2023.

## Placed in

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

## Builds on (most cited first, 27 of 27)

- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [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)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Diffusion Models for Implicit Image Segmentation Ensembles](https://mlsanity.com/paper/2112.03145/) (2021)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [Soft Diffusion: Score Matching for General Corruptions](https://mlsanity.com/paper/2209.05442/) (2022)
- [Blurring Diffusion Models](https://mlsanity.com/paper/2209.05557/) (2022)
- [Progressive Deblurring of Diffusion Models for Coarse-to-Fine Image Synthesis](https://mlsanity.com/paper/2207.11192/) (2022)
- [Generalized Normalizing Flows via Markov Chains](https://mlsanity.com/paper/2111.12506/) (2021)
- [Explicit Diffusion of Gaussian Mixture Model Based Image Priors](https://mlsanity.com/paper/2302.08411/) (2023)
- [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)
- [Quantisation Scale-Spaces](https://mlsanity.com/paper/2103.10491/) (2021)
- [Image Blending with Osmosis](https://mlsanity.com/paper/2303.07762/) (2023)
- [Generalised Scale-Space Properties for Probabilistic Diffusion Models](https://mlsanity.com/paper/2303.07900/) (2023)

## Abstract (arXiv)

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.