# Diffusion models with location-scale noise

arXiv: https://arxiv.org/abs/2304.05907 · HTML: https://mlsanity.com/paper/2304.05907/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 6 of its 7 references that are in the map.
- First posted on arXiv 12 Apr 2023.

## Placed in

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

## Builds on (most cited first, 6 of 6)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Estimating the Optimal Covariance with Imperfect Mean in Diffusion Probabilistic Models](https://mlsanity.com/paper/2206.07309/) (2022)
- [Heavy-tailed denoising score matching](https://mlsanity.com/paper/2112.09788/) (2021)

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

- [Blue noise for diffusion models](https://mlsanity.com/paper/2402.04930/) (2024)
- [Stimulating Diffusion Model for Image Denoising via Adaptive Embedding and Ensembling](https://mlsanity.com/paper/2307.03992/) (2023)
- [SDDPM: Speckle Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2311.10868/) (2023)
- [PixelBoost: Leveraging Brownian Motion for Realistic-Image Super-Resolution](https://mlsanity.com/paper/2506.23254/) (2025)
- [Mat'ern Noise for Triangulation-Agnostic Flow Matching on Meshes](https://mlsanity.com/paper/2605.19305/) (2026)
- [Annealed L'evy Diffusion via Gaussian Surrogate Reverse Dynamics](https://mlsanity.com/paper/2610.19692/) (2026)

## Abstract (arXiv)

Diffusion Models (DMs) are powerful generative models that add Gaussian noise to the data and learn to remove it. We wanted to determine which noise distribution (Gaussian or non-Gaussian) led to better generated data in DMs. Since DMs do not work by design with non-Gaussian noise, we built a framework that allows reversing a diffusion process with non-Gaussian location-scale noise. We use that framework to show that the Gaussian distribution performs the best over a wide range of other distributions (Laplace, Uniform, t, Generalized-Gaussian).