mlsanityData to 14 Oct 2026

Wavelet Score-Based Generative Modeling

arXiv 2208.05003 ↗First posted 9 Aug 2022cs.LG cs.CV stat.MLcited by 62

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Score-based generative models (SGMs) synthesize new data samples from Gaussian white noise by running a time-reversed Stochastic Differential Equation (SDE) whose drift coefficient depends on some probabilistic score. The discretization of such SDEs typically requires a large number of time steps and hence a high computational cost. This is because of ill-conditioning properties of the score that we analyze mathematically. We show that SGMs can be considerably accelerated, by factorizing the data distribution into a product of conditional probabilities of wavelet coefficients across scales. The resulting Wavelet Score-based Generative Model (WSGM) synthesizes wavelet coefficients with the same number of time steps at all scales, and its time complexity therefore grows linearly with the image size. This is proved mathematically over Gaussian distributions, and shown numerically over physical processes at phase transition and natural image datasets.

Key facts. Cited by 62 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 33 of its 65 references that are in the map. First posted on arXiv 9 Aug 2022.

Builds on

33 of 65 references.

Closest ancestors · 17

Same direction, newest first

  1. 2022Subspace Diffusion Generative Models3 May
  2. 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
  3. 2022Pseudo Numerical Methods for Diffusion Models on Manifolds20 Feb
  4. 2021Tackling the Generative Learning Trilemma with Denoising Diffusion GANs15 Dec
  5. 2021Non Gaussian Denoising Diffusion Models14 Jun
  6. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  7. 2021On Fast Sampling of Diffusion Probabilistic Models31 May
  8. 2021Cascaded Diffusion Models for High Fidelity Image Generation30 May
  9. 2021Gotta Go Fast When Generating Data with Score-Based Models28 May
  10. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  11. 2021Noise Estimation for Generative Diffusion Models6 Apr
  12. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
5 more
  1. 2021Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed7 Jan
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  3. 2020Denoising Diffusion Implicit Models6 Oct
  4. 2020Denoising Diffusion Probabilistic Models19 Jun
  5. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 16

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  3. 2014Deep Learning Face Attributes in the Wildcited by 3,693
  4. 2017Progressive Growing of GANs for Improved Quality, Stability, and Variationcited by 2,988
  5. 2021Image Super-Resolution via Iterative Refinementcited by 1,511
  6. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,354
  7. 2018On the Spectral Bias of Neural Networkscited by 1,341
  8. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 622
  9. 2021Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speechcited by 447
  10. 2017GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibriumcited by 213
  11. 2014A* Samplingcited by 151
  12. 2020Solving Linear Inverse Problems Using the Prior Implicit in a Denoisercited by 79
4 more
  1. 2020Wavelet Flow: Fast Training of High Resolution Normalizing Flowscited by 33
  2. 2022Wavelet Conditional Renormalization Groupcited by 11
  3. 2017Learning a Wavelet-like Auto-Encoder to Accelerate Deep Neural Networkscited by 8
  4. 2021Learning Non-linear Wavelet Transformation via Normalizing Flowcited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 3; 2023: 16; 2024: 18; 2025: 15; 2026: 10.

62 papers.

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  1. 2024Diffusion Model-Based Image Editing: A Surveycited by 212
  2. 2024Dynamical Regimes of Diffusion Modelscited by 142
  3. 2022Wavelet Diffusion Models are fast and scalable Image Generatorscited by 117
  4. 2023Score-based Diffusion Models in Function Spacecited by 82
  5. 2023Long-Term Photometric Consistent Novel View Synthesis with Diffusion Modelscited by 76
  6. 2024Wavelet Convolutions for Large Receptive Fieldscited by 74
  7. 2025Diffusion-4K: Ultra-High-Resolution Image Synthesis with Latent Diffusion Modelscited by 65
  8. 2024Diffusion Models, Image Super-Resolution And Everything: A Surveycited by 64
  9. 2024WDM: 3D Wavelet Diffusion Models for High-Resolution Medical Image Synthesiscited by 56
  10. 2024Boosting Diffusion Models with Moving Average Sampling in Frequency Domaincited by 55
  11. 2025A Fourier Space Perspective on Diffusion Modelscited by 52
  12. 2023WaveDM: Wavelet-Based Diffusion Models for Image Restorationcited by 47
38 more
  1. 2023Infinite-Dimensional Diffusion Modelscited by 39
  2. 2022Fast Graph Generation via Spectral Diffusioncited by 36
  3. 2023Synthetic Lagrangian Turbulence by Generative Diffusion Modelscited by 32
  4. 2025Accelerated Diffusion Models via Speculative Samplingcited by 31
  5. 2024Wavelet Diffusion Neural Operatorcited by 29
  6. 2023A Unified Framework for U-Net Design and Analysiscited by 27
  7. 2024Enhancing Foundation Models for Time Series Forecasting via Wavelet-based Tokenizationcited by 27
  8. 2022Spectral Diffusion Processescited by 25
  9. 2024LiteVAE: Lightweight and Efficient Variational Autoencoders for Latent Diffusion Modelscited by 22
  10. 2023Learning multi-scale local conditional probability models of imagescited by 21
  11. 2023Waving Goodbye to Low-Res: A Diffusion-Wavelet Approach for Image Super-Resolutioncited by 19
  12. 2023Generative modeling for time series via Schr"odinger bridgecited by 18
  13. 2025Lipschitz-Guided Design of Interpolation Schedules in Generative Modelscited by 17
  14. 2023Renormalizing Diffusion Modelscited by 16
  15. 2023Geometric Neural Diffusion Processescited by 10
  16. 2023Fr'echet Wavelet Distance: A Domain-Agnostic Metric for Image Generationcited by 9
  17. 2024Wavelets Are All You Need for Autoregressive Image Generationcited by 9
  18. 2023Image generation with shortest path diffusioncited by 8
  19. 2024TriNeRFLet: A Wavelet Based Triplane NeRF Representationcited by 8
  20. 2025fastWDM3D: Fast and Accurate 3D Healthy Tissue Inpaintingcited by 8
  21. 2025Decoupling High and Low Frequencies for Faithful Image Generation with Fine Detailscited by 7
  22. 2023Product of Gaussian Mixture Diffusion Modelscited by 6
  23. 2023UDPM: Upsampling Diffusion Probabilistic Modelscited by 5
  24. 2025Ultra-High-Resolution Image Synthesis: Data, Method and Evaluationcited by 5
  25. 2025Scale-Adaptive Generative Flows for Multiscale Scientific Datacited by 5
  26. 2024Universal randomised signatures for generative time series modellingcited by 4
  27. 2024GUD: Generation with Unified Diffusioncited by 4
  28. 2024A Wavelet Diffusion GAN for Image Super-Resolutioncited by 4
  29. 2024Hierarchic Flows to Estimate and Sample High-dimensional Probabilitiescited by 3
  30. 2024Critically Damped Third-Order Langevin Dynamicscited by 3
  31. 2025Critically-Damped Higher-Order Langevin Dynamics for Generative Modelingcited by 3
  32. 2025WaveletDiff: Multilevel Wavelet Diffusion For Time Series Generationcited by 3
  33. 2026WaiT for the Signal: Simple Frequency-Aware Flow-Matchingcited by 3
  34. 2023Conditionally Strongly Log-Concave Generative Modelscited by 2
  35. 2024Multi-scale Conditional Generative Modeling for Microscopic Image Restorationcited by 2
  36. 2024Multi-scale Generative Modeling for Fast Samplingcited by 2
  37. 2025Likelihood Training of Cascaded Diffusion Models via Hierarchical Volume-preserving Mapscited by 2
  38. 2025Computationally Efficient Diffusion Models in Medical Imaging: A Comprehensive Reviewcited by 1

50 most cited of 62 All 62 (JSON)

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  1. 2022Convergence of score-based generative modeling for general data distributions
  2. 2024Score-based Generative Models with Adaptive Momentum
  3. 2022Accelerating Score-based Generative Models for High-Resolution Image Synthesis
  4. 2022Convergence for score-based generative modeling with polynomial complexity
  5. 2024A Good Score Does not Lead to A Good Generative Model
  6. 2026Non-asymptotic Convergence of Stochastic Gradient Descent in Score-based Generative Models
  7. 2024Score-based generative models break the curse of dimensionality in learning a family of sub-Gaussian probability distributions
  8. 2023Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models