# Gradient Domain Diffusion Models for Image Synthesis

arXiv: https://arxiv.org/abs/2309.01875 · HTML: https://mlsanity.com/paper/2309.01875/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 16 of its 49 references that are in the map.
- First posted on arXiv 5 Sep 2023.

## Placed in

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

## Builds on (most cited first, 16 of 16)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [LLaMA-Adapter: Efficient Fine-tuning of Language Models with Zero-init Attention](https://mlsanity.com/paper/2303.16199/) (2023)
- [Dynamic Neural Networks: A Survey](https://mlsanity.com/paper/2102.04906/) (2021)
- [Training Language Models with Language Feedback at Scale](https://mlsanity.com/paper/2303.16755/) (2023)
- [Side Window Filtering](https://mlsanity.com/paper/1905.07177/) (2019)
- [What do Large Language Models Learn about Scripts?](https://mlsanity.com/paper/2112.13834/) (2021)
- [Weighted Mean Curvature](https://mlsanity.com/paper/1903.07189/) (2019)
- [Fast and High-Quality Blind Multi-Spectral Image Pansharpening](https://mlsanity.com/paper/2103.09943/) (2021)
- [A Discrete Scheme for Computing Image's Weighted Gaussian Curvature](https://mlsanity.com/paper/2101.07927/) (2021)
- [SERF: Towards better training of deep neural networks using log-Softplus ERror activation Function](https://mlsanity.com/paper/2108.09598/) (2021)
- [Quarter Laplacian Filter for Edge Aware Image Processing](https://mlsanity.com/paper/2101.07933/) (2021)
- [Dynamic Large Language Models on Blockchains](https://mlsanity.com/paper/2307.10549/) (2023)
- [Multilevel Large Language Models for Everyone](https://mlsanity.com/paper/2307.13221/) (2023)

## Built on by (most cited first, 4 of 4)

- [Functional Imaging Constrained Diffusion for Brain PET Synthesis from Structural MRI](https://mlsanity.com/paper/2405.02504/) (2024)
- [Mjolnir: Breaking the Shield of Perturbation-Protected Gradients via Adaptive Diffusion](https://mlsanity.com/paper/2407.05285/) (2024)
- [GDGS: Gradient Domain Gaussian Splatting for Sparse Representation of Radiance Fields](https://mlsanity.com/paper/2405.05446/) (2024)
- [TWIG: Two-Step Image Generation using Segmentation Masks in Diffusion Models](https://mlsanity.com/paper/2504.14933/) (2025)

## Abstract (arXiv)

Diffusion models are getting popular in generative image and video synthesis. However, due to the diffusion process, they require a large number of steps to converge. To tackle this issue, in this paper, we propose to perform the diffusion process in the gradient domain, where the convergence becomes faster. There are two reasons. First, thanks to the Poisson equation, the gradient domain is mathematically equivalent to the original image domain. Therefore, each diffusion step in the image domain has a unique corresponding gradient domain representation. Second, the gradient domain is much sparser than the image domain. As a result, gradient domain diffusion models converge faster. Several numerical experiments confirm that the gradient domain diffusion models are more efficient than the original diffusion models. The proposed method can be applied in a wide range of applications such as image processing, computer vision and machine learning tasks.