mlsanityData to 14 Oct 2026

Score-based Denoising Diffusion with Non-Isotropic Gaussian Noise Models

arXiv 2210.12254 ↗First posted 21 Oct 2022cs.LG cs.CVcited by 17

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Generative models based on denoising diffusion techniques have led to an unprecedented increase in the quality and diversity of imagery that is now possible to create with neural generative models. However, most contemporary state-of-the-art methods are derived from a standard isotropic Gaussian formulation. In this work we examine the situation where non-isotropic Gaussian distributions are used. We present the key mathematical derivations for creating denoising diffusion models using an underlying non-isotropic Gaussian noise model. We also provide initial experiments with the CIFAR-10 dataset to help verify empirically that this more general modeling approach can also yield high-quality samples.

Key facts. Cited by 17 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 23 references that are in the map. First posted on arXiv 21 Oct 2022.

Builds on

16 of 23 references.

Closest ancestors · 6

Same direction, newest first

  1. 2021Denoising Diffusion Gamma Models10 Oct
  2. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  4. 2020Denoising Diffusion Implicit Models6 Oct
  5. 2020Denoising Diffusion Probabilistic Models19 Jun
  6. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 10

  1. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  2. 2022Video Diffusion Modelscited by 2,305
  3. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,354
  4. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 622
  5. 2022MCVD: Masked Conditional Video Diffusion for Prediction, Generation, and Interpolationcited by 309
  6. 2022Diffusion Probabilistic Modeling for Video Generationcited by 238
  7. 2022Generative Modelling With Inverse Heat Dissipationcited by 167
  8. 2020Adversarial score matching and improved sampling for image generationcited by 96
  9. 2022Poisson Flow Generative Modelscited by 95
  10. 2019Neural Empirical Bayescited by 46

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 6; 2024: 3; 2025: 4; 2026: 3.

17 papers.

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  1. 2023Score-based Diffusion Models in Function Spacecited by 82
  2. 2023On the Design Fundamentals of Diffusion Models: A Surveycited by 60
  3. 2025A Fourier Space Perspective on Diffusion Modelscited by 52
  4. 2023Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generationcited by 37
  5. 2024Blue noise for diffusion modelscited by 29
  6. 2023Memory in Plain Sight: Surveying the Uncanny Resemblances of Associative Memories and Diffusion Modelscited by 13
  7. 2025Nonisotropic Gaussian Diffusion for Realistic 3D Human Motion Predictioncited by 12
  8. 2023Geometric Neural Diffusion Processescited by 10
  9. 2024Edge-preserving noise for diffusion modelscited by 6
  10. 2023Multi-Resolution Diffusion for Privacy-Sensitive Recommender Systemscited by 4
  11. 2024GUD: Generation with Unified Diffusioncited by 4
  12. 2025Learning What Matters: Steering Diffusion via Spectrally Anisotropic Forward Noisecited by 2
5 more
  1. 2025Deep Neural Networks Inspired by Differential Equationscited by 2
  2. 2026Colorful-Noise: Training-Free Low-Frequency Noise Manipulation for Color-Based Conditional Image Generationcited by 1
  3. 2022Posterior sampling with CNN-based, Plug-and-Play regularization with applications to Post-Stack Seismic Inversioncited by 0
  4. 2026Phi-Noise: Training-Free Temporal Video Conditioning via Phase-Based Noise Manipulationcited by 0
  5. 2026Noise in Diffusion Models Is a Learnable Inputcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023Diffusion Model for Generative Image Denoising
  2. 2021Non Gaussian Denoising Diffusion Models
  3. 2022Diffusion Models in Vision: A Survey
  4. 2025Denoising Score Distillation: From Noisy Diffusion Pretraining to One-Step High-Quality Generation
  5. 2023SVNR: Spatially-variant Noise Removal with Denoising Diffusion
  6. 2026Efficient and Training-Free Single-Image Diffusion Models
  7. 2023Denoising Diffusion Bridge Models
  8. 2022From Denoising Diffusions to Denoising Markov Models