mlsanityData to 7 Oct 2026

Diffusion map particle systems for generative modeling

arXiv 2304.00200 ↗First posted 1 Apr 2023stat.ML cs.LG stat.COcited by 6

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Abstract (arXiv)

We propose a novel diffusion map particle system (DMPS) for generative modeling, based on diffusion maps and Laplacian-adjusted Wasserstein gradient descent (LAWGD). Diffusion maps are used to approximate the generator of the corresponding Langevin diffusion process from samples, and hence to learn the underlying data-generating manifold. On the other hand, LAWGD enables efficient sampling from the target distribution given a suitable choice of kernel, which we construct here via a spectral approximation of the generator, computed with diffusion maps. Our method requires no offline training and minimal tuning, and can outperform other approaches on data sets of moderate dimension.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 32 of its 62 references that are in the map. First posted on arXiv 1 Apr 2023.

Builds on

32 of 62 references.

References · 32

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  5. 2016Improved Techniques for Training GANscited by 2,938
  6. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  7. 2021Cascaded Diffusion Models for High Fidelity Image Generationcited by 1,155
  8. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  9. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  10. 2022Diffusion-LM Improves Controllable Text Generationcited by 1,006
  11. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  12. 2019SinGAN: Learning a Generative Model from a Single Natural Imagecited by 348
20 more
  1. 2019Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Designcited by 258
  2. 2018Generative Adversarial Network in Medical Imaging: A Reviewcited by 257
  3. 2017MMD GAN: Towards Deeper Understanding of Moment Matching Networkcited by 251
  4. 2020Learning Gradient Fields for Shape Generationcited by 245
  5. 2022Riemannian Score-Based Generative Modellingcited by 216
  6. 2016Semantic Image Inpainting with Deep Generative Modelscited by 156
  7. 2017Stein Variational Gradient Descent as Gradient Flowcited by 149
  8. 2018Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problemcited by 123
  9. 2022Score-Based Generative Models Detect Manifoldscited by 121
  10. 2020Flows for simultaneous manifold learning and density estimationcited by 117
  11. 2021An Introduction to Deep Generative Modelingcited by 104
  12. 2016Medical Image Synthesis with Context-Aware Generative Adversarial Networkscited by 91
  13. 2018GANs for Medical Image Analysiscited by 81
  14. 2020SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergencecited by 64
  15. 2021Rectangular Flows for Manifold Learningcited by 49
  16. 2021Particle Cloud Generation with Message Passing Generative Adversarial Networkscited by 45
  17. 2021Protein sequence design with deep generative modelscited by 35
  18. 2022How Much is Enough? A Study on Diffusion Times in Score-based Generative Modelscited by 35
  19. 2017Generative and Discriminative Text Classification with Recurrent Neural Networkscited by 30
  20. 2016Language as a Latent Variable: Discrete Generative Models for Sentence Compressioncited by 28

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 1; 2025: 2; 2026: 2.

6 papers.

  1. 2024A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systemscited by 19
  2. 2025Bifidelity Parameter Estimation Using Conditional Diffusion Modelscited by 7
  3. 2023MESSY Estimation: Maximum-Entropy based Stochastic and Symbolic densitY Estimationcited by 5
  4. 2025Generative Modeling through Koopman Spectral Analysis: An Operator-Theoretic Perspectivecited by 0
  5. 2026Diffusion Processes on Implicit Manifoldscited by 0
  6. 2026Adaptive Kernel Selection for Kernelized Diffusion Mapscited by 0