# Elucidating the Design Space of Arbitrary-Noise-Based Diffusion Models

arXiv: https://arxiv.org/abs/2507.18534 · HTML: https://mlsanity.com/paper/2507.18534/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 30 of its 43 references that are in the map.
- First posted on arXiv 24 Jul 2025.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## 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)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [BBDM: Image-to-image Translation with Brownian Bridge Diffusion Models](https://mlsanity.com/paper/2205.07680/) (2022)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)
- [Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration](https://mlsanity.com/paper/2303.11435/) (2023)
- [Stacked Conditional Generative Adversarial Networks for Jointly Learning Shadow Detection and Shadow Removal](https://mlsanity.com/paper/1712.02478/) (2017)
- [Towards Ghost-free Shadow Removal via Dual Hierarchical Aggregation Network and Shadow Matting GAN](https://mlsanity.com/paper/1911.08718/) (2019)
- [Refusion: Enabling Large-Size Realistic Image Restoration with Latent-Space Diffusion Models](https://mlsanity.com/paper/2304.08291/) (2023)
- [Auto-Exposure Fusion for Single-Image Shadow Removal](https://mlsanity.com/paper/2103.01255/) (2021)
- [Residual Denoising Diffusion Models](https://mlsanity.com/paper/2308.13712/) (2023)
- [DuDoNet: Dual Domain Network for CT Metal Artifact Reduction](https://mlsanity.com/paper/1907.00273/) (2019)
- [From Shadow Generation to Shadow Removal](https://mlsanity.com/paper/2103.12997/) (2021)
- [Diffusion Bridge Implicit Models](https://mlsanity.com/paper/2405.15885/) (2024)
- [Deep Lesion Graphs in the Wild: Relationship Learning and Organization of Significant Radiology Image Findings in a Diverse Large-scale Lesion Database](https://mlsanity.com/paper/1711.10535/) (2017)
- [Deep Sinogram Completion with Image Prior for Metal Artifact Reduction in CT Images](https://mlsanity.com/paper/2009.07469/) (2020)
- [ShadowFormer: Global Context Helps Image Shadow Removal](https://mlsanity.com/paper/2302.01650/) (2023)
- [ADN: Artifact Disentanglement Network for Unsupervised Metal Artifact Reduction](https://mlsanity.com/paper/1908.01104/) (2019)
- [Improving Shadow Suppression for Illumination Robust Face Recognition](https://mlsanity.com/paper/1710.05073/) (2017)
- [CT sinogram-consistency learning for metal-induced beam hardening correction](https://mlsanity.com/paper/1708.00607/) (2017)
- [InDuDoNet+: A Deep Unfolding Dual Domain Network for Metal Artifact Reduction in CT Images](https://mlsanity.com/paper/2112.12660/) (2021)
- [Reversing Flow for Image Restoration](https://mlsanity.com/paper/2506.16961/) (2025)
- [LapGM: A Multisequence MR Bias Correction and Normalization Model](https://mlsanity.com/paper/2209.13619/) (2022)

## Abstract (arXiv)

Although EDM aims to unify the design space of diffusion models, its reliance on fixed Gaussian noise prevents it from explaining emerging flow-based methods that diffuse arbitrary noise. Moreover, our study reveals that EDM's forcible injection of Gaussian noise has adverse effects on image restoration task, as it corrupts the degraded images, overextends the restoration distance, and increases the task's complexity. To interpret diverse methods for handling distinct noise patterns within a unified theoretical framework and to minimize the restoration distance, we propose EDA, which Elucidates the Design space of Arbitrary-noise diffusion models. Theoretically, EDA expands noise pattern flexibility while preserving EDM's modularity, with rigorous proof that increased noise complexity introduces no additional computational overhead during restoration. EDA is validated on three representative medical image denoising and natural image restoration tasks: MRI bias field correction (global smooth noise), CT metal artifact removal (global sharp noise) and natural image shadow removal (local boundary-aware noise). With only 5 sampling steps, competitive results against specialized methods across medical and natural tasks demonstrate EDA's strong generalization capability for image restoration. Code is available at: https://github.com/PerceptionComputingLab/EDA.