# Denoising Diffusion Gamma Models

arXiv: https://arxiv.org/abs/2110.05948 · HTML: https://mlsanity.com/paper/2110.05948/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 30 of its 38 references that are in the map.
- First posted on arXiv 10 Oct 2021.

## Placed in

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

## Builds on (most cited first, 30 of 30)

- [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)
- [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)
- [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)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [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)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speech](https://mlsanity.com/paper/2105.06337/) (2021)
- [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)
- [A Variational Perspective on Diffusion-Based Generative Models and Score Matching](https://mlsanity.com/paper/2106.02808/) (2021)
- [On Fast Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.00132/) (2021)
- [Learning to Efficiently Sample from Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.03802/) (2021)
- [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)
- [Bilateral Denoising Diffusion Models](https://mlsanity.com/paper/2108.11514/) (2021)

## Built on by (most cited first, 27 of 27)

- [MCVD: Masked Conditional Video Diffusion for Prediction, Generation, and Interpolation](https://mlsanity.com/paper/2205.09853/) (2022)
- [Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration](https://mlsanity.com/paper/2303.11435/) (2023)
- [Soft Diffusion: Score Matching for General Corruptions](https://mlsanity.com/paper/2209.05442/) (2022)
- [A Survey on Audio Diffusion Models: Text To Speech Synthesis and Enhancement in Generative AI](https://mlsanity.com/paper/2303.13336/) (2023)
- [On the Design Fundamentals of Diffusion Models: A Survey](https://mlsanity.com/paper/2306.04542/) (2023)
- [Consistent Diffusion Models: Mitigating Sampling Drift by Learning to be Consistent](https://mlsanity.com/paper/2302.09057/) (2023)
- [Efficient Diffusion Models for Vision: A Survey](https://mlsanity.com/paper/2210.09292/) (2022)
- [Iterative α-(de)Blending: a Minimalist Deterministic Diffusion Model](https://mlsanity.com/paper/2305.03486/) (2023)
- [Maximum Likelihood Training of Implicit Nonlinear Diffusion Models](https://mlsanity.com/paper/2205.13699/) (2022)
- [Diffusion Models for Audio Restoration](https://mlsanity.com/paper/2402.09821/) (2024)
- [Dynamic Dual-Output Diffusion Models](https://mlsanity.com/paper/2203.04304/) (2022)
- [Variational Control for Guidance in Diffusion Models](https://mlsanity.com/paper/2502.03686/) (2025)
- [Heavy-Tailed Diffusion with Denoising L'evy Probabilistic Models](https://mlsanity.com/paper/2407.18609/) (2024)
- [Score-based Denoising Diffusion with Non-Isotropic Gaussian Noise Models](https://mlsanity.com/paper/2210.12254/) (2022)
- [DiracDiffusion: Denoising and Incremental Reconstruction with Assured Data-Consistency](https://mlsanity.com/paper/2303.14353/) (2023)
- [Star-Shaped Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2302.05259/) (2023)
- [FlexiDiT: Your Diffusion Transformer Can Easily Generate High-Quality Samples with Less Compute](https://mlsanity.com/paper/2502.20126/) (2025)
- [Generative modelling with jump-diffusions](https://mlsanity.com/paper/2503.06558/) (2025)
- [Diffusion Models with Heavy-Tailed Targets: Score Estimation and Sampling Guarantees](https://mlsanity.com/paper/2601.06715/) (2026)
- [DiffLoad: Uncertainty Quantification in Electrical Load Forecasting with the Diffusion Model](https://mlsanity.com/paper/2306.01001/) (2023)
- [Dale meets Langevin: A Multiplicative Denoising Diffusion Model](https://mlsanity.com/paper/2510.02730/) (2025)
- [GARD: Gamma-based Anatomical Restoration and Denoising for Retinal OCT](https://mlsanity.com/paper/2509.10341/) (2025)
- [Exploiting Intermediate Reconstructions in Optical Coherence Tomography for Test-Time Adaption of Medical Image Segmentation](https://mlsanity.com/paper/2603.05041/) (2026)
- [VVRec: Reconstruction Attacks on DL-based Volumetric Video Upstreaming via Latent Diffusion Model with Gamma Distribution](https://mlsanity.com/paper/2502.17880/) (2025)
- [Diffusion Models under Alternative Noise: Simplified Analysis and Sensitivity](https://mlsanity.com/paper/2506.08337/) (2025)
- [Region-Adaptive Generative Compression with Spatially Varying Diffusion Models](https://mlsanity.com/paper/2604.01122/) (2026)
- [γ-Bridge: A Look-Parametric Diffusion Bridge](https://mlsanity.com/paper/2607.22719/) (2026)

## Abstract (arXiv)

Generative diffusion processes are an emerging and effective tool for image and speech generation. In the existing methods, the underlying noise distribution of the diffusion process is Gaussian noise. However, fitting distributions with more degrees of freedom could improve the performance of such generative models. In this work, we investigate other types of noise distribution for the diffusion process. Specifically, we introduce the Denoising Diffusion Gamma Model (DDGM) and show that noise from Gamma distribution provides improved results for image and speech generation. Our approach preserves the ability to efficiently sample state in the training diffusion process while using Gamma noise.