mlsanityData to 7 Oct 2026

Deep MMD Gradient Flow without adversarial training

arXiv 2405.06780 ↗First posted 10 May 2024cs.LG cs.AIcited by 18

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Abstract (arXiv)

We propose a gradient flow procedure for generative modeling by transporting particles from an initial source distribution to a target distribution, where the gradient field on the particles is given by a noise-adaptive Wasserstein Gradient of the Maximum Mean Discrepancy (MMD). The noise-adaptive MMD is trained on data distributions corrupted by increasing levels of noise, obtained via a forward diffusion process, as commonly used in denoising diffusion probabilistic models. The result is a generalization of MMD Gradient Flow, which we call Diffusion-MMD-Gradient Flow or DMMD. The divergence training procedure is related to discriminator training in Generative Adversarial Networks (GAN), but does not require adversarial training. We obtain competitive empirical performance in unconditional image generation on CIFAR10, MNIST, CELEB-A (64 x64) and LSUN Church (64 x 64). Furthermore, we demonstrate the validity of the approach when MMD is replaced by a lower bound on the KL divergence.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). Builds on 54 of its 80 references that are in the map. First posted on arXiv 10 May 2024.

Builds on

54 of 80 references.

References · 54

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  3. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  6. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  7. 2022Generative Adversarial Networkscited by 5,603
  8. 2022Flow Matching for Generative Modelingcited by 5,426
  9. 2017Neural Discrete Representation Learningcited by 4,650
  10. 2014Going Deeper with Convolutionscited by 4,231
  11. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  12. 2019Analyzing and Improving the Image Quality of StyleGANcited by 3,580
38 more
  1. 2022DreamFusion: Text-to-3D using 2D Diffusioncited by 3,006
  2. 2016Improved Techniques for Training GANscited by 2,938
  3. 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,609
  4. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
  5. 2017Improved Training of Wasserstein GANscited by 2,223
  6. 2023Consistency Modelscited by 1,778
  7. 2022Imagen Video: High Definition Video Generation with Diffusion Modelscited by 1,765
  8. 2015LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loopcited by 1,350
  9. 2018Demystifying MMD GANscited by 1,268
  10. 2020Training Generative Adversarial Networks with Limited Datacited by 1,184
  11. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  12. 2023Adversarial Diffusion Distillationcited by 741
  13. 2018Which Training Methods for GANs do actually Converge?cited by 672
  14. 2021Tackling the Generative Learning Trilemma with Denoising Diffusion GANscited by 515
  15. 2016f-GAN: Training Generative Neural Samplers using Variational Divergence Minimizationcited by 504
  16. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 440
  17. 2023Voicebox: Text-Guided Multilingual Universal Speech Generation at Scalecited by 373
  18. 2017Learning Generative Models with Sinkhorn Divergencescited by 310
  19. 2022Cold Diffusion: Inverting Arbitrary Image Transforms Without Noisecited by 275
  20. 2017MMD GAN: Towards Deeper Understanding of Moment Matching Networkcited by 251
  21. 2022Convergence of denoising diffusion models under the manifold hypothesiscited by 237
  22. 2017Generalization and Equilibrium in Generative Adversarial Nets (GANs)cited by 165
  23. 2023UFOGen: You Forward Once Large Scale Text-to-Image Generation via Diffusion GANscited by 165
  24. 2019Maximum Mean Discrepancy Gradient Flowcited by 123
  25. 2022Score-Based Generative Models Detect Manifoldscited by 121
  26. 2022Soft Diffusion: Score Matching for General Corruptionscited by 101
  27. 2020Generalized Energy Based Modelscited by 73
  28. 2020Your GAN is Secretly an Energy-based Model and You Should use Discriminator Driven Latent Samplingcited by 71
  29. 2021Variational Wasserstein gradient flowcited by 53
  30. 2017On the Discrimination-Generalization Tradeoff in GANscited by 48
  31. 2020Generative Adversarial Networks for Image and Video Synthesis: Algorithms and Applicationscited by 48
  32. 2020Refining Deep Generative Models via Discriminator Gradient Flowcited by 45
  33. 2021KALE Flow: A Relaxed KL Gradient Flow for Probabilities with Disjoint Supportcited by 37
  34. 2023Generative Sliced MMD Flows with Riesz Kernelscited by 36
  35. 2023On Error Propagation of Diffusion Modelscited by 30
  36. 2018On gradient regularizers for MMD GANscited by 28
  37. 2023Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernelcited by 25
  38. 2021A Neural Tangent Kernel Perspective of GANscited by 21

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 7; 2026: 8.

18 papers.

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  1. 2025Distributional Diffusion Models with Scoring Rulescited by 25
  2. 2025Scale-wise Distillation of Diffusion Modelscited by 11
  3. 2024Fast Summation of Radial Kernels via QMC Slicingcited by 7
  4. 2026On the Wasserstein Gradient Flow Interpretation of Drifting Modelscited by 6
  5. 2024Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamicscited by 4
  6. 2025Training Latent Diffusion Models with Interacting Particle Algorithmscited by 4
  7. 2024Statistical and Geometrical properties of regularized Kernel Kullback-Leibler divergencecited by 3
  8. 2026Sobolev Regularized MMD Gradient Flowcited by 3
  9. 2025Stationary MMD Pointscited by 2
  10. 2025Sequence Modeling with Spectral Mean Flowscited by 2
  11. 2026Three-Body Scattering for Generative Modelingcited by 2
  12. 2025ReLU integral probability metric and its applicationscited by 1
6 more
  1. 2026Improved Distributional Diffusion Modelscited by 1
  2. 2025One-shot Conditional Sampling: MMD meets Nearest Neighborscited by 0
  3. 2026A Gradient Flow Perspective on Minimum MMD Estimationcited by 0
  4. 2026Sharp Convergence of Wasserstein Gradient Flows for Spectrally Nonnegative Interaction Energiescited by 0
  5. 2026Interacting particle guidance for sampling reward-tilted generative priorscited by 0
  6. 2026Improving Function Space Flow Matching with Kernel Optimal Transportcited by 0

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  3. 2025Diffusion Models: A Mathematical Introduction
  4. 2024Adv-KD: Adversarial Knowledge Distillation for Faster Diffusion Sampling
  5. 2023DiffFlow: A Unified SDE Framework for Score-Based Diffusion Models and Generative Adversarial Networks
  6. 2022Truncated Diffusion Probabilistic Models and Diffusion-based Adversarial Auto-Encoders
  7. 2026One-Step Generative Modeling via Wasserstein Gradient Flows
  8. 2024Steering Rectified Flow Models in the Vector Field for Controlled Image Generation