# Squeezed Diffusion Models

arXiv: https://arxiv.org/abs/2508.14871 · HTML: https://mlsanity.com/paper/2508.14871/

## 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 11 of its 20 references that are in the map.
- First posted on arXiv 20 Aug 2025.

## Placed in

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

## Builds on (most cited first, 11 of 11)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [On the Importance of Noise Scheduling for Diffusion Models](https://mlsanity.com/paper/2301.10972/) (2023)
- [Wavelet Diffusion Models are fast and scalable Image Generators](https://mlsanity.com/paper/2211.16152/) (2022)
- [A Fourier Space Perspective on Diffusion Models](https://mlsanity.com/paper/2505.11278/) (2025)
- [Diffusion Models With Learned Adaptive Noise](https://mlsanity.com/paper/2312.13236/) (2023)
- [Blue noise for diffusion models](https://mlsanity.com/paper/2402.04930/) (2024)

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

- [Information Theoretic Learning for Diffusion Models with Warm Start](https://mlsanity.com/paper/2510.20903/) (2025)

## Abstract (arXiv)

Diffusion models typically inject isotropic Gaussian noise, disregarding structure in the data. Motivated by the way quantum squeezed states redistribute uncertainty according to the Heisenberg uncertainty principle, we introduce Squeezed Diffusion Models (SDM), which scale noise anisotropically along the principal component of the training distribution. As squeezing enhances the signal-to-noise ratio in physics, we hypothesize that scaling noise in a data-dependent manner can better assist diffusion models in learning important data features. We study two configurations: (i) a Heisenberg diffusion model that compensates the scaling on the principal axis with inverse scaling on orthogonal directions and (ii) a standard SDM variant that scales only the principal axis. Counterintuitively, on CIFAR-10/100 and CelebA-64, mild antisqueezing - i.e. increasing variance on the principal axis - consistently improves FID by up to 15% and shifts the precision-recall frontier toward higher recall. Our results demonstrate that simple, data-aware noise shaping can deliver robust generative gains without architectural changes.