# Blue noise for diffusion models

arXiv: https://arxiv.org/abs/2402.04930 · HTML: https://mlsanity.com/paper/2402.04930/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 32 of its 47 references that are in the map.
- First posted on arXiv 7 Feb 2024.

## Placed in

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

## Builds on (most cited first, 30 of 32)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [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)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [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)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [Exposing flaws of generative model evaluation metrics and their unfair treatment of diffusion models](https://mlsanity.com/paper/2306.04675/) (2023)
- [On the Importance of Noise Scheduling for Diffusion Models](https://mlsanity.com/paper/2301.10972/) (2023)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [State of the Art on Diffusion Models for Visual Computing](https://mlsanity.com/paper/2310.07204/) (2023)
- [Wavelet Diffusion Models are fast and scalable Image Generators](https://mlsanity.com/paper/2211.16152/) (2022)
- [Iterative α-(de)Blending: a Minimalist Deterministic Diffusion Model](https://mlsanity.com/paper/2305.03486/) (2023)
- [Score-based Denoising Diffusion with Non-Isotropic Gaussian Noise Models](https://mlsanity.com/paper/2210.12254/) (2022)
- [Gaussian Blue Noise](https://mlsanity.com/paper/2206.07798/) (2022)
- [Diffusion models with location-scale noise](https://mlsanity.com/paper/2304.05907/) (2023)

## Built on by (most cited first, 29 of 29)

- [Fast, Scale-Adaptive, and Uncertainty-Aware Downscaling of Earth System Model Fields with Generative Machine Learning](https://mlsanity.com/paper/2403.02774/) (2024)
- [Nonisotropic Gaussian Diffusion for Realistic 3D Human Motion Prediction](https://mlsanity.com/paper/2501.06035/) (2025)
- [SeaCache: Spectral-Evolution-Aware Cache for Accelerating Diffusion Models](https://mlsanity.com/paper/2602.18993/) (2026)
- [Edge-preserving noise for diffusion models](https://mlsanity.com/paper/2410.01540/) (2024)
- [Infinite-Resolution Integral Noise Warping for Diffusion Models](https://mlsanity.com/paper/2411.01212/) (2024)
- [On Equivariance and Fast Sampling in Video Diffusion Models Trained with Warped Noise](https://mlsanity.com/paper/2504.09789/) (2025)
- [Spectrally-Guided Diffusion Noise Schedules](https://mlsanity.com/paper/2603.19222/) (2026)
- [Improved Immiscible Diffusion: Accelerate Diffusion Training by Reducing Its Miscibility](https://mlsanity.com/paper/2505.18521/) (2025)
- [Harmonizing Geometry and Uncertainty: Diffusion with Hyperspheres](https://mlsanity.com/paper/2506.10576/) (2025)
- [MotionCrafter: Dense Geometry and Motion Reconstruction with a 4D VAE](https://mlsanity.com/paper/2602.08961/) (2026)
- [Learning What Matters: Steering Diffusion via Spectrally Anisotropic Forward Noise](https://mlsanity.com/paper/2510.09660/) (2025)
- [LumiTex: Towards High-Fidelity PBR Texture Generation with Illumination Context](https://mlsanity.com/paper/2511.19437/) (2025)
- [Generative Modeling with Orbit-Space Particle Flow Matching](https://mlsanity.com/paper/2605.02222/) (2026)
- [Colored Noise Diffusion Sampling](https://mlsanity.com/paper/2605.30332/) (2026)
- [Optimal Transport Flow Matching by Design](https://mlsanity.com/paper/2606.04092/) (2026)
- [CoCA: Step-level Reward for Free in RL-based T2I Diffusion Model Fine-tuning](https://mlsanity.com/paper/2505.19196/) (2025)
- [Beyond Blur: A Fluid Perspective on Generative Diffusion Models](https://mlsanity.com/paper/2506.16827/) (2025)
- [Squeezed Diffusion Models](https://mlsanity.com/paper/2508.14871/) (2025)
- [Variational Trajectory Optimization of Anisotropic Diffusion Schedules](https://mlsanity.com/paper/2602.19512/) (2026)
- [Colorful-Noise: Training-Free Low-Frequency Noise Manipulation for Color-Based Conditional Image Generation](https://mlsanity.com/paper/2605.00548/) (2026)
- [Optimizing Visual Generative Models via Distribution-wise Rewards](https://mlsanity.com/paper/2607.02291/) (2026)
- [I-Diff: Structural Regularization for High-Fidelity Diffusion Models](https://mlsanity.com/paper/2403.16790/) (2024)
- [Training-free, Perceptually Consistent Low-Resolution Previews with High-Resolution Image for Efficient Workflows of Diffusion Models](https://mlsanity.com/paper/2604.09227/) (2026)
- [Mat'ern Noise for Triangulation-Agnostic Flow Matching on Meshes](https://mlsanity.com/paper/2605.19305/) (2026)
- [Phi-Noise: Training-Free Temporal Video Conditioning via Phase-Based Noise Manipulation](https://mlsanity.com/paper/2605.24509/) (2026)
- [Low-Pass Flow Matching](https://mlsanity.com/paper/2606.02177/) (2026)
- [Flicker-DDPM: Accelerating Denoising Diffusion via 1/f Colored Noise Injection](https://mlsanity.com/paper/2606.03393/) (2026)
- [Noise in Diffusion Models Is a Learnable Input](https://mlsanity.com/paper/2608.02575/) (2026)
- [PRISM: Principled Reference Identification for Schrodinger Bridge Model](https://mlsanity.com/paper/2608.06893/) (2026)

## Abstract (arXiv)

Most of the existing diffusion models use Gaussian noise for training and sampling across all time steps, which may not optimally account for the frequency contents reconstructed by the denoising network. Despite the diverse applications of correlated noise in computer graphics, its potential for improving the training process has been underexplored. In this paper, we introduce a novel and general class of diffusion models taking correlated noise within and across images into account. More specifically, we propose a time-varying noise model to incorporate correlated noise into the training process, as well as a method for fast generation of correlated noise mask. Our model is built upon deterministic diffusion models and utilizes blue noise to help improve the generation quality compared to using Gaussian white (random) noise only. Further, our framework allows introducing correlation across images within a single mini-batch to improve gradient flow. We perform both qualitative and quantitative evaluations on a variety of datasets using our method, achieving improvements on different tasks over existing deterministic diffusion models in terms of FID metric.