# Non Gaussian Denoising Diffusion Models

arXiv: https://arxiv.org/abs/2106.07582 · HTML: https://mlsanity.com/paper/2106.07582/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 20 of its 29 references that are in the map.
- First posted on arXiv 14 Jun 2021.

## Placed in

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

## Builds on (most cited first, 20 of 20)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [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)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Adversarial Audio Synthesis](https://mlsanity.com/paper/1802.04208/) (2018)
- [Efficient Neural Audio Synthesis](https://mlsanity.com/paper/1802.08435/) (2018)
- [Learning Energy-Based Models by Diffusion Recovery Likelihood](https://mlsanity.com/paper/2012.08125/) (2020)
- [High Fidelity Speech Synthesis with Adversarial Networks](https://mlsanity.com/paper/1909.11646/) (2019)

## Built on by (most cited first, 30 of 45)

- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Repurposing Diffusion-Based Image Generators for Monocular Depth Estimation](https://mlsanity.com/paper/2312.02145/) (2023)
- [A Comprehensive Survey of AI-Generated Content (AIGC): A History of Generative AI from GAN to ChatGPT](https://mlsanity.com/paper/2303.04226/) (2023)
- [Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality](https://mlsanity.com/paper/2202.05830/) (2022)
- [GENIE: Higher-Order Denoising Diffusion Solvers](https://mlsanity.com/paper/2210.05475/) (2022)
- [DiffPose: Toward More Reliable 3D Pose Estimation](https://mlsanity.com/paper/2211.16940/) (2022)
- [Optimizing DDPM Sampling with Shortcut Fine-Tuning](https://mlsanity.com/paper/2301.13362/) (2023)
- [Progressive Distillation for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2202.00512/) (2022)
- [Unifying Diffusion Models' Latent Space, with Applications to CycleDiffusion and Guidance](https://mlsanity.com/paper/2210.05559/) (2022)
- [Wavelet Score-Based Generative Modeling](https://mlsanity.com/paper/2208.05003/) (2022)
- [On the Design Fundamentals of Diffusion Models: A Survey](https://mlsanity.com/paper/2306.04542/) (2023)
- [Efficient Diffusion Models for Vision: A Survey](https://mlsanity.com/paper/2210.09292/) (2022)
- [Maximum Likelihood Training of Implicit Nonlinear Diffusion Models](https://mlsanity.com/paper/2205.13699/) (2022)
- [Sampling, Diffusions, and Stochastic Localization](https://mlsanity.com/paper/2305.10690/) (2023)
- [Unraveling the Smoothness Properties of Diffusion Models: A Gaussian Mixture Perspective](https://mlsanity.com/paper/2405.16418/) (2024)
- [Entropy-driven Sampling and Training Scheme for Conditional Diffusion Generation](https://mlsanity.com/paper/2206.11474/) (2022)
- [Fast Sampling via Discrete Non-Markov Diffusion Models with Predetermined Transition Time](https://mlsanity.com/paper/2312.09193/) (2023)
- [Heavy-tailed denoising score matching](https://mlsanity.com/paper/2112.09788/) (2021)
- [Stage-by-stage Wavelet Optimization Refinement Diffusion Model for Sparse-View CT Reconstruction](https://mlsanity.com/paper/2308.15942/) (2023)
- [Gaussian Mixture Solvers for Diffusion Models](https://mlsanity.com/paper/2311.00941/) (2023)
- [A Complete Recipe for Diffusion Generative Models](https://mlsanity.com/paper/2303.01748/) (2023)
- [DPoser: Diffusion Model as Robust 3D Human Pose Prior](https://mlsanity.com/paper/2312.05541/) (2023)
- [Generative Diffusion Models for Wireless Networks: Fundamental, Architecture, and State-of-the-Art](https://mlsanity.com/paper/2507.16733/) (2025)
- [Memory in Plain Sight: Surveying the Uncanny Resemblances of Associative Memories and Diffusion Models](https://mlsanity.com/paper/2309.16750/) (2023)
- [Structured Diffusion Models with Mixture of Gaussians as Prior Distribution](https://mlsanity.com/paper/2410.19149/) (2024)
- [SDDPM: Speckle Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2311.10868/) (2023)
- [Improved DDIM Sampling with Moment Matching Gaussian Mixtures](https://mlsanity.com/paper/2311.04938/) (2023)
- [Fully Spiking Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2312.01742/) (2023)
- [Improved probabilistic regression using diffusion models](https://mlsanity.com/paper/2510.04583/) (2025)

## Abstract (arXiv)

Generative diffusion processes are an emerging and effective tool for image and speech generation. In the existing methods, the underline noise distribution of the diffusion process is Gaussian noise. However, fitting distributions with more degrees of freedom, could help the performance of such generative models. In this work, we investigate other types of noise distribution for the diffusion process. Specifically, we show that noise from Gamma distribution provides improved results for image and speech generation. Moreover, we show that using a mixture of Gaussian noise variables in the diffusion process improves the performance over a diffusion process that is based on a single distribution. Our approach preserves the ability to efficiently sample state in the training diffusion process while using Gamma noise and a mixture of noise.