# Edge-preserving noise for diffusion models

arXiv: https://arxiv.org/abs/2410.01540 · HTML: https://mlsanity.com/paper/2410.01540/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 26 of its 37 references that are in the map.
- First posted on arXiv 2 Oct 2024.

## Placed in

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

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [MaskGAN: Towards Diverse and Interactive Facial Image Manipulation](https://mlsanity.com/paper/1907.11922/) (2019)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Score-Based Generative Modeling with Critically-Damped Langevin Diffusion](https://mlsanity.com/paper/2112.07068/) (2021)
- [Exposing flaws of generative model evaluation metrics and their unfair treatment of diffusion models](https://mlsanity.com/paper/2306.04675/) (2023)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [Soft Diffusion: Score Matching for General Corruptions](https://mlsanity.com/paper/2209.05442/) (2022)
- [Blurring Diffusion Models](https://mlsanity.com/paper/2209.05557/) (2022)
- [Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --](https://mlsanity.com/paper/2301.03362/) (2023)
- [WaveDM: Wavelet-Based Diffusion Models for Image Restoration](https://mlsanity.com/paper/2305.13819/) (2023)
- [Blue noise for diffusion models](https://mlsanity.com/paper/2402.04930/) (2024)
- [An Improved Evaluation Framework for Generative Adversarial Networks](https://mlsanity.com/paper/1803.07474/) (2018)
- [Score-based Denoising Diffusion with Non-Isotropic Gaussian Noise Models](https://mlsanity.com/paper/2210.12254/) (2022)

## Built on by (most cited first, 6 of 6)

- [ItDPDM: Information-Theoretic Discrete Poisson Diffusion Model](https://mlsanity.com/paper/2505.05082/) (2025)
- [Deep Neural Networks Inspired by Differential Equations](https://mlsanity.com/paper/2510.09685/) (2025)
- [GEWDiff: Geometric Enhanced Wavelet-based Diffusion Model for Hyperspectral Image Super-resolution](https://mlsanity.com/paper/2511.07103/) (2025)
- [Variational Trajectory Optimization of Anisotropic Diffusion Schedules](https://mlsanity.com/paper/2602.19512/) (2026)
- [HyperNet-Adaptation for Diffusion-Based Test Case Generation](https://mlsanity.com/paper/2601.15041/) (2026)
- [Decoupled Drift-Diffusion World Models for Consistent Future Frame Prediction](https://mlsanity.com/paper/2610.19212/) (2026)

## Abstract (arXiv)

Classical diffusion models typically rely on isotropic Gaussian noise, treating all regions uniformly and overlooking structural information important for high-quality generation. We introduce an edge-preserving diffusion process that generalizes isotropic models via a hybrid noise scheme with an edge-aware scheduler that smoothly transitions from edge-preserving to isotropic noise. This enables the model to capture fine structural details while generally maintaining global performance. We evaluate the impact of structure-aware noise in both diffusion and flow-matching frameworks, and show that existing isotropic models can be efficiently fine-tuned with edge-preserving noise, making our framework practical for adapting pre-trained systems. Beyond unconditional generation, our method particularly shows improvements in structure-guided tasks such as stroke-to-image synthesis, improving robustness and perceptual quality, as evidenced by consistent improvements across FID, KID, and CLIP-score.