mlsanityData to 14 Oct 2026

Fast Sampling of Diffusion Models via Operator Learning

arXiv 2211.13449 ↗First posted 24 Nov 2022cs.LG cs.CVcited by 175

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion models have found widespread adoption in various areas. However, their sampling process is slow because it requires hundreds to thousands of network evaluations to emulate a continuous process defined by differential equations. In this work, we use neural operators, an efficient method to solve the probability flow differential equations, to accelerate the sampling process of diffusion models. Compared to other fast sampling methods that have a sequential nature, we are the first to propose a parallel decoding method that generates images with only one model forward pass. We propose diffusion model sampling with neural operator (DSNO) that maps the initial condition, i.e., Gaussian distribution, to the continuous-time solution trajectory of the reverse diffusion process. To model the temporal correlations along the trajectory, we introduce temporal convolution layers that are parameterized in the Fourier space into the given diffusion model backbone. We show our method achieves state-of-the-art FID of 3.78 for CIFAR-10 and 7.83 for ImageNet-64 in the one-model-evaluation setting.

Key facts. Cited by 175 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 36 of its 47 references that are in the map. First posted on arXiv 24 Nov 2022.

Builds on

36 of 47 references.

Closest ancestors · 20

Same direction, newest first

  1. 2022GENIE: Higher-Order Denoising Diffusion Solvers11 Oct
  2. 2022On Distillation of Guided Diffusion Models6 Oct
  3. 2022All are Worth Words: A ViT Backbone for Diffusion Models25 Sep
  4. 2022Estimating the Optimal Covariance with Imperfect Mean in Diffusion Probabilistic Models15 Jun
  5. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  6. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  7. 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
  8. 2022Pseudo Numerical Methods for Diffusion Models on Manifolds20 Feb
  9. 2022Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality11 Feb
  10. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models17 Jan
  11. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  12. 2021Tackling the Generative Learning Trilemma with Denoising Diffusion GANs15 Dec
8 more
  1. 2021Bilateral Denoising Diffusion Models26 Aug
  2. 2021Score-based Generative Modeling in Latent Space10 Jun
  3. 2021On Fast Sampling of Diffusion Probabilistic Models31 May
  4. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  5. 2021Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed7 Jan
  6. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  7. 2020Denoising Diffusion Implicit Models6 Oct
  8. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 16

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  3. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,177
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  5. 2022Generative Adversarial Networkscited by 5,627
  6. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  7. 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,626
  8. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,354
  9. 2019Improved Precision and Recall Metric for Assessing Generative Modelscited by 944
  10. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
  11. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 516
  12. 2022Diffusion Models for Adversarial Purificationcited by 476
4 more
  1. 2021Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speechcited by 447
  2. 2021Neural Operator: Learning Maps Between Function Spacescited by 414
  3. 2022(Certified!!) Adversarial Robustness for Free!cited by 132
  4. 2021Seismic wave propagation and inversion with Neural Operatorscited by 51

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 42; 2024: 71; 2025: 47; 2026: 15.

175 papers.

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  1. 2023Consistency Modelscited by 1,822
  2. 2023One-step Diffusion with Distribution Matching Distillationcited by 1,019
  3. 2023Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inferencecited by 846
  4. 2024Improved Distribution Matching Distillation for Fast Image Synthesiscited by 684
  5. 2023Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusioncited by 459
  6. 2023Improved Techniques for Training Consistency Modelscited by 439
  7. 2023DeepCache: Accelerating Diffusion Models for Freecited by 359
  8. 2024Simplifying, Stabilizing and Scaling Continuous-Time Consistency Modelscited by 283
  9. 2023SinSR: Diffusion-Based Image Super-Resolution in a Single Stepcited by 238
  10. 2023Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Modelscited by 236
  11. 2024Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generationcited by 214
  12. 2023Fast Training of Diffusion Models with Masked Transformerscited by 176
38 more
  1. 2024Consistency Models Made Easycited by 144
  2. 2023TRACT: Denoising Diffusion Models with Transitive Closure Time-Distillationcited by 116
  3. 2024One-Step Image Translation with Text-to-Image Modelscited by 116
  4. 2025Inductive Moment Matchingcited by 113
  5. 2024Is Sora a World Simulator? A Comprehensive Survey on General World Models and Beyondcited by 111
  6. 2023Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscalingcited by 110
  7. 2023Diffusion Models for Image Restoration and Enhancement: A Comprehensive Surveycited by 109
  8. 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency modelscited by 109
  9. 2024Improving the Training of Rectified Flowscited by 108
  10. 2024Consistency Flow Matching: Defining Straight Flows with Velocity Consistencycited by 104
  11. 2025How to build a consistency model: Learning flow maps via self-distillationcited by 103
  12. 2024Align Your Steps: Optimizing Sampling Schedules in Diffusion Modelscited by 96
  13. 2023Compositional Foundation Models for Hierarchical Planningcited by 95
  14. 2023Minimizing Trajectory Curvature of ODE-based Generative Modelscited by 89
  15. 2024One-Step Diffusion Policy: Fast Visuomotor Policies via Diffusion Distillationcited by 89
  16. 2024T2V-Turbo: Breaking the Quality Bottleneck of Video Consistency Model with Mixed Reward Feedbackcited by 87
  17. 2025Align Your Flow: Scaling Continuous-Time Flow Map Distillationcited by 87
  18. 2024Distilling Diffusion Models into Conditional GANscited by 78
  19. 2023A Mathematical Guide to Operator Learningcited by 76
  20. 2024One-Step Diffusion Distillation through Score Implicit Matchingcited by 71
  21. 2024Multistep Consistency Modelscited by 67
  22. 2024EM Distillation for One-step Diffusion Modelscited by 62
  23. 2023One-Step Diffusion Distillation via Deep Equilibrium Modelscited by 61
  24. 2023On the Design Fundamentals of Diffusion Models: A Surveycited by 60
  25. 2023StreamDiffusion: A Pipeline-level Solution for Real-time Interactive Generationcited by 58
  26. 2024Flash Diffusion: Accelerating Any Conditional Diffusion Model for Few Steps Image Generationcited by 56
  27. 2024On the Trajectory Regularity of ODE-based Diffusion Samplingcited by 55
  28. 2024Distillation of Discrete Diffusion through Dimensional Correlationscited by 48
  29. 2023On Exact Inversion of DPM-Solverscited by 47
  30. 2024Adversarial Score identity Distillation: Rapidly Surpassing the Teacher in One Stepcited by 47
  31. 2025Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithmscited by 47
  32. 2023A Comprehensive Survey on Knowledge Distillation of Diffusion Modelscited by 45
  33. 2024Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modellingcited by 45
  34. 2025One-step Diffusion Models with f-Divergence Distribution Matchingcited by 43
  35. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexitycited by 42
  36. 2024Equivariant Graph Neural Operator for Modeling 3D Dynamicscited by 38
  37. 2023Bespoke Solvers for Generative Flow Modelscited by 37
  38. 2025LBM: Latent Bridge Matching for Fast Image-to-Image Translationcited by 36

50 most cited of 175 All 175 (JSON)

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  1. 2025TADA: Improved Diffusion Sampling with Training-free Augmented Dynamics
  2. 2025ODEt(ODEl): Shortcutting the Time and the Length in Diffusion and Flow Models for Faster Sampling
  3. 2023Accelerating Guided Diffusion Sampling with Splitting Numerical Methods
  4. 2024An Ordinary Differential Equation Sampler with Stochastic Start for Diffusion Bridge Models
  5. 2023Fast ODE-based Sampling for Diffusion Models in Around 5 Steps
  6. 2025Are First-Order Diffusion Samplers Really Slower? A Fast Forward-Value Approach
  7. 2023Reflected Diffusion Models
  8. 2022Diffusion Models in Vision: A Survey