mlsanityData to 14 Oct 2026

Generative Modelling With Inverse Heat Dissipation

arXiv 2206.13397 ↗First posted 21 Jun 2022cs.CV cs.LG stat.MLcited by 167

Not on the map. Why?

Cited by 128 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

While diffusion models have shown great success in image generation, their noise-inverting generative process does not explicitly consider the structure of images, such as their inherent multi-scale nature. Inspired by diffusion models and the empirical success of coarse-to-fine modelling, we propose a new diffusion-like model that generates images through stochastically reversing the heat equation, a PDE that locally erases fine-scale information when run over the 2D plane of the image. We interpret the solution of the forward heat equation with constant additive noise as a variational approximation in the diffusion latent variable model. Our new model shows emergent qualitative properties not seen in standard diffusion models, such as disentanglement of overall colour and shape in images. Spectral analysis on natural images highlights connections to diffusion models and reveals an implicit coarse-to-fine inductive bias in them.

Key facts. Cited by 167 papers in the map (data through 14 Oct 2026). Builds on 66 of its 93 references that are in the map. First posted on arXiv 21 Jun 2022.

Builds on

66 of 93 references.

References · 66

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  3. 2020Denoising Diffusion Implicit Modelscited by 9,781
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  7. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
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  9. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 6,013
  10. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  11. 2013Auto-Encoding Variational Bayescited by 4,053
  12. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
38 more
  1. 2019Analyzing and Improving the Image Quality of StyleGANcited by 3,588
  2. 2017Progressive Growing of GANs for Improved Quality, Stability, and Variationcited by 2,988
  3. 2022Video Diffusion Modelscited by 2,305
  4. 2016Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Networkcited by 1,908
  5. 2021Image Super-Resolution via Iterative Refinementcited by 1,511
  6. 2019Generating Diverse High-Fidelity Images with VQ-VAE-2cited by 1,387
  7. 2015LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loopcited by 1,355
  8. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,354
  9. 2021Alias-Free Generative Adversarial Networkscited by 1,184
  10. 2021Cascaded Diffusion Models for High Fidelity Image Generationcited by 1,163
  11. 2021Variational Diffusion Modelscited by 1,153
  12. 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,098
  13. 2016Geometric deep learning: going beyond Euclidean datacited by 1,048
  14. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,043
  15. 2022Denoising Diffusion Restoration Modelscited by 963
  16. 2016Conditional Image Generation with PixelCNN Decoderscited by 862
  17. 2016Pixel Recurrent Neural Networkscited by 816
  18. 2018Image Transformercited by 772
  19. 2021Diffusion Probabilistic Models for 3D Point Cloud Generationcited by 735
  20. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 672
  21. 2020NVAE: A Deep Hierarchical Variational Autoencodercited by 637
  22. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 622
  23. 2020GANSpace: Discovering Interpretable GAN Controlscited by 614
  24. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 602
  25. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 574
  26. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 521
  27. 20213D Shape Generation and Completion through Point-Voxel Diffusioncited by 516
  28. 2022StyleGAN-XL: Scaling StyleGAN to Large Diverse Datasetscited by 492
  29. 2017PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modificationscited by 417
  30. 2017DeblurGAN: Blind Motion Deblurring Using Conditional Adversarial Networkscited by 367
  31. 2019DeblurGAN-v2: Deblurring (Orders-of-Magnitude) Faster and Bettercited by 362
  32. 2021Score-based diffusion models for accelerated MRIcited by 311
  33. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contractioncited by 307
  34. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 286
  35. 2020Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Imagescited by 264
  36. 2021Deblurring via Stochastic Refinementcited by 249
  37. 2020Learning Gradient Fields for Shape Generationcited by 245
  38. 2022Diffusion Probabilistic Modeling for Video Generationcited by 238

50 most cited of 66 All 66 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 10; 2023: 39; 2024: 33; 2025: 49; 2026: 36.

167 papers.

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  1. 2022Cold Diffusion: Inverting Arbitrary Image Transforms Without Noisecited by 276
  2. 2022A Survey on Generative Diffusion Modelcited by 240
  3. 2024FlowEdit: Inversion-Free Text-Based Editing Using Pre-Trained Flow Modelscited by 217
  4. 2023Image Restoration with Mean-Reverting Stochastic Differential Equationscited by 183
  5. 2023Single-Stage Diffusion NeRF: A Unified Approach to 3D Generation and Reconstructioncited by 180
  6. 2022Improving Sample Quality of Diffusion Models Using Self-Attention Guidancecited by 154
  7. 2022Towards the Detection of Diffusion Model Deepfakescited by 111
  8. 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecastingcited by 109
  9. 2025DDT: Decoupled Diffusion Transformercited by 109
  10. 2025Mogao: An Omni Foundation Model for Interleaved Multi-Modal Generationcited by 109
  11. 2022Soft Diffusion: Score Matching for General Corruptionscited by 102
  12. 2022Blurring Diffusion Modelscited by 91
38 more
  1. 2023Minimizing Trajectory Curvature of ODE-based Generative Modelscited by 89
  2. 2024Variational Flow Matching for Graph Generationcited by 83
  3. 2023Score-based Diffusion Models in Function Spacecited by 82
  4. 2025Improving the Diffusability of Autoencoderscited by 80
  5. 2023Relay Diffusion: Unifying diffusion process across resolutions for image synthesiscited by 79
  6. 2023Matryoshka Diffusion Modelscited by 72
  7. 2024A Survey on Diffusion Models for Time Series and Spatio-Temporal Datacited by 67
  8. 2023On the Design Fundamentals of Diffusion Models: A Surveycited by 60
  9. 2025A Fourier Space Perspective on Diffusion Modelscited by 52
  10. 2023Diffusion Models With Learned Adaptive Noisecited by 51
  11. 2024Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modellingcited by 45
  12. 2023Stable Target Field for Reduced Variance Score Estimation in Diffusion Modelscited by 44
  13. 2024CleanDIFT: Diffusion Features without Noisecited by 44
  14. 2024RF-Diffusion: Radio Signal Generation via Time-Frequency Diffusioncited by 42
  15. 2023Continuous-Time Functional Diffusion Processescited by 39
  16. 2023Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generationcited by 37
  17. 2022Progressive Deblurring of Diffusion Models for Coarse-to-Fine Image Synthesiscited by 34
  18. 2024Switti: Designing Scale-Wise Transformers for Text-to-Image Synthesiscited by 33
  19. 2022f-DM: A Multi-stage Diffusion Model via Progressive Signal Transformationcited by 32
  20. 2024Blue noise for diffusion modelscited by 29
  21. 2023Diffusion Probabilistic Fieldscited by 28
  22. 2024Fast, Scale-Adaptive, and Uncertainty-Aware Downscaling of Earth System Model Fields with Generative Machine Learningcited by 27
  23. 2025"Principal Components" Enable A New Language of Imagescited by 27
  24. 2024Probing the Latent Hierarchical Structure of Data via Diffusion Modelscited by 26
  25. 2025An Analytical Theory of Spectral Bias in the Learning Dynamics of Diffusion Modelscited by 26
  26. 2022Spectral Diffusion Processescited by 25
  27. 2023Graph Signal Diffusion Model for Collaborative Filteringcited by 25
  28. 2023∞-Diff: Infinite Resolution Diffusion with Subsampled Mollified Statescited by 21
  29. 2023Unpaired Downscaling of Fluid Flows with Diffusion Bridgescited by 21
  30. 2023Blind Audio Bandwidth Extension: A Diffusion-Based Zero-Shot Approachcited by 21
  31. 2023Neural Diffusion Modelscited by 21
  32. 2023GenPhys: From Physical Processes to Generative Modelscited by 19
  33. 2023Learning to Jump: Thinning and Thickening Latent Counts for Generative Modelingcited by 18
  34. 2025Semantics Lead the Way: Harmonizing Semantic and Texture Modeling with Asynchronous Latent Diffusioncited by 18
  35. 2022Score-based Denoising Diffusion with Non-Isotropic Gaussian Noise Modelscited by 17
  36. 2023Beta Diffusioncited by 17
  37. 2023DiffEnc: Variational Diffusion with a Learned Encodercited by 17
  38. 2023Solving Inverse Physics Problems with Score Matchingcited by 16

50 most cited of 167 All 167 (JSON)

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  4. 2026A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Models
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