# Explicit Diffusion of Gaussian Mixture Model Based Image Priors

arXiv: https://arxiv.org/abs/2302.08411 · HTML: https://mlsanity.com/paper/2302.08411/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 20 references that are in the map.
- First posted on arXiv 16 Feb 2023.

## Builds on (most cited first, 3 of 3)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems](https://mlsanity.com/paper/1702.02505/) (2017)

## Built on by (most cited first, 6 of 6)

- [Diffusion models for Gaussian distributions: Exact solutions and Wasserstein errors](https://mlsanity.com/paper/2405.14250/) (2024)
- [Learning from small data sets: Patch-based regularizers in inverse problems for image reconstruction](https://mlsanity.com/paper/2312.16611/) (2023)
- [Structured Diffusion Models with Mixture of Gaussians as Prior Distribution](https://mlsanity.com/paper/2410.19149/) (2024)
- [Product of Gaussian Mixture Diffusion Models](https://mlsanity.com/paper/2310.12653/) (2023)
- [Joint Non-Linear MRI Inversion with Diffusion Priors](https://mlsanity.com/paper/2310.14842/) (2023)
- [Generalised Diffusion Probabilistic Scale-Spaces](https://mlsanity.com/paper/2309.08511/) (2023)

## Abstract (arXiv)

In this work we tackle the problem of estimating the density fX of a random variable X by successive smoothing, such that the smoothed random variable Y fulfills (partialt - Delta1)fY(,·,, t) = 0, fY(,·,, 0) = fX. With a focus on image processing, we propose a product/fields of experts model with Gaussian mixture experts that admits an analytic expression for fY (,·,, t) under an orthogonality constraint on the filters. This construction naturally allows the model to be trained simultaneously over the entire diffusion horizon using empirical Bayes. We show preliminary results on image denoising where our model leads to competitive results while being tractable, interpretable, and having only a small number of learnable parameters. As a byproduct, our model can be used for reliable noise estimation, allowing blind denoising of images corrupted by heteroscedastic noise.