mlsanityData to 7 Oct 2026

Sampling, Diffusions, and Stochastic Localization

arXiv 2305.10690 ↗First posted 18 May 2023cs.LGcited by 38

Not on the map. Why?

Cited by 31 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a sample from the target distribution. The drift of the diffusion process is typically represented as a neural network. Stochastic localization is a successful technique to prove mixing of Markov Chains and other functional inequalities in high dimension. An algorithmic version of stochastic localization was recently proposed in order to sample from certain statistical mechanics models. This expository article has three objectives: (i)~Generalize the algorithmic construction to other stochastic localization processes. This construction is both simple and broadly applicable; (ii)~Clarify the connection between diffusions and stochastic localization. This allows to derive several known sampling schemes in a unified fashion; (iii)~Describe the insights that follow from this unified viewpoint.

Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). Builds on 23 of its 44 references that are in the map. First posted on arXiv 18 May 2023.

Builds on

23 of 44 references.

References · 23

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Denoising Diffusion Implicit Modelscited by 9,655
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  5. 2022Flow Matching for Generative Modelingcited by 5,426
  6. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  7. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  8. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  9. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  10. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  11. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 566
  12. 2022DiGress: Discrete Denoising diffusion for graph generationcited by 503
11 more
  1. 2022A Continuous Time Framework for Discrete Denoising Modelscited by 437
  2. 2022Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioningcited by 362
  3. 2022Score-based Continuous-time Discrete Diffusion Modelscited by 167
  4. 2022Concrete Score Matching: Generalized Score Matching for Discrete Datacited by 144
  5. 2017The power of sum-of-squares for detecting hidden structurescited by 54
  6. 2022Sampling from the Sherrington-Kirkpatrick Gibbs measure via algorithmic stochastic localizationcited by 48
  7. 2021Non Gaussian Denoising Diffusion Modelscited by 43
  8. 2020Computational Barriers to Estimation from Low-Degree Polynomialscited by 38
  9. 2018Reducibility and Computational Lower Bounds for Problems with Planted Sparse Structurecited by 35
  10. 2022First Hitting Diffusion Models for Generating Manifold, Graph and Categorical Datacited by 18
  11. 2021Heavy-tailed denoising score matchingcited by 17

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 6; 2024: 12; 2025: 10; 2026: 10.

38 papers.

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  1. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localizationcited by 230
  2. 2024An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimizationcited by 72
  3. 2024Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theorycited by 58
  4. 2024Minimax Optimality of Score-based Diffusion Models: Beyond the Density Lower Bound Assumptionscited by 45
  5. 2024Learning general Gaussian mixtures with efficient score matchingcited by 43
  6. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexitycited by 42
  7. 2023Reverse Diffusion Monte Carlocited by 41
  8. 2024Learning Mixtures of Gaussians Using Diffusion Modelscited by 41
  9. 2023Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Modelscited by 39
  10. 2023The statistical thermodynamics of generative diffusion models: Phase transitions, symmetry breaking and critical instabilitycited by 37
  11. 2024Manifolds, Random Matrices and Spectral Gaps: The geometric phases of generative diffusioncited by 31
  12. 2024Losing dimensions: Geometric memorization in generative diffusioncited by 28
26 more
  1. 2024Provable Acceleration for Diffusion Models under Minimal Assumptionscited by 27
  2. 2023Sampling with flows, diffusion and autoregressive neural networks: A spin-glass perspectivecited by 26
  3. 2023Improved Convergence of Score-Based Diffusion Models via Prediction-Correctioncited by 23
  4. 2024U-Nets as Belief Propagation: Efficient Classification, Denoising, and Diffusion in Generative Hierarchical Modelscited by 17
  5. 2025The Information Dynamics of Generative Diffusioncited by 12
  6. 2025Diffusion Models are Secretly Exchangeable: Parallelizing DDPMs via Autospeculationcited by 11
  7. 2025Improving the evaluation of samplers on multi-modal targetscited by 9
  8. 2026The Entropic Signature of Class Speciation in Diffusion Modelscited by 7
  9. 2025Information-Theoretic Proofs for Diffusion Samplingcited by 6
  10. 2024Denoising Diffusions with Optimal Transport: Localization, Curvature, and Multi-Scale Complexitycited by 5
  11. 2025Parallel Sampling via Autospeculationcited by 5
  12. 2026Steering Dynamical Regimes of Diffusion Models by Breaking Detailed Balancecited by 3
  13. 2025Computational bottlenecks for denoising diffusionscited by 2
  14. 2025Joint stochastic localization and applicationscited by 2
  15. 2025Perspectives on Stochastic Localizationcited by 2
  16. 2026Low-Dimensional Adaptation of Rectified Flow: A Diffusion and Stochastic Localization Perspectivecited by 2
  17. 2026Denoising growth complexity: Data geometry and certified schedules for diffusion samplingcited by 2
  18. 2025Generative diffusion for perceptron problems: statistical physics analysis and efficient algorithmscited by 1
  19. 2025Generating solution paths of Markovian stochastic differential equations using diffusion modelscited by 1
  20. 2026Score Shocks: The Burgers Equation Structure of Diffusion Generative Modelscited by 1
  21. 2026A Mathematical Introduction to Diffusion Modelscited by 1
  22. 2024Towards understanding Diffusion Models (on Graphs)cited by 0
  23. 2026Binomial flows: Denoising and flow matching for discrete ordinal datacited by 0
  24. 2026Connections between the F"ollmer process and the denoising diffusion probabilistic modelcited by 0
  25. 2026On McDiarmid's Inequality under Dependence via Approximate Tensorization of Entropycited by 0
  26. 2026Simulation-free and finite-time diffusion modelcited by 0