mlsanityData to 7 Oct 2026

Stochastic Localization via Iterative Posterior Sampling

arXiv 2402.10758 ↗First posted 16 Feb 2024stat.ML cs.LG stat.COcited by 27

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Abstract (arXiv)

Building upon score-based learning, new interest in stochastic localization techniques has recently emerged. In these models, one seeks to noise a sample from the data distribution through a stochastic process, called observation process, and progressively learns a denoiser associated to this dynamics. Apart from specific applications, the use of stochastic localization for the problem of sampling from an unnormalized target density has not been explored extensively. This work contributes to fill this gap. We consider a general stochastic localization framework and introduce an explicit class of observation processes, associated with flexible denoising schedules. We provide a complete methodology, textitStochastic Localization via Iterative Posterior Sampling (SLIPS), to obtain approximate samples of this dynamics, and as a by-product, samples from the target distribution. Our scheme is based on a Markov chain Monte Carlo estimation of the denoiser and comes with detailed practical guidelines. We illustrate the benefits and applicability of SLIPS on several benchmarks of multi-modal distributions, including Gaussian mixtures in increasing dimensions, Bayesian logistic regression and a high-dimensional field system from statistical-mechanics.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). Builds on 37 of its 73 references that are in the map. First posted on arXiv 16 Feb 2024.

Builds on

37 of 73 references.

References · 37

  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. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  5. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  6. 2021GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Modelscited by 3,595
  7. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  8. 2015Variational Inference with Normalizing Flowscited by 2,161
  9. 2021Variational Diffusion Modelscited by 1,145
  10. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  11. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 620
  12. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
25 more
  1. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 440
  2. 2023Understanding Diffusion Objectives as the ELBO with Simple Data Augmentationcited by 293
  3. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
  4. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 195
  5. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 175
  6. 2022An optimal control perspective on diffusion-based generative modelingcited by 145
  7. 2023Denoising Diffusion Samplerscited by 144
  8. 2018Log-concave sampling: Metropolis-Hastings algorithms are fastcited by 117
  9. 2023Improved sampling via learned diffusionscited by 103
  10. 2019Theoretical guarantees for sampling and inference in generative models with latent diffusionscited by 97
  11. 2021Bayesian Learning via Neural Schr"odinger-F"ollmer Flowscited by 56
  12. 2022Score-Based Diffusion meets Annealed Importance Samplingcited by 51
  13. 2022Sampling from the Sherrington-Kirkpatrick Gibbs measure via algorithmic stochastic localizationcited by 48
  14. 2019Neural Empirical Bayescited by 46
  15. 2019Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein Distancecited by 43
  16. 2023Reverse Diffusion Monte Carlocited by 41
  17. 2018Metropolis-Hastings Generative Adversarial Networkscited by 40
  18. 2022Langevin Diffusion Variational Inferencecited by 26
  19. 2023Sampling with flows, diffusion and autoregressive neural networks: A spin-glass perspectivecited by 26
  20. 2023Transport meets Variational Inference: Controlled Monte Carlo Diffusionscited by 21
  21. 2023On Sampling with Approximate Transport Mapscited by 20
  22. 2023Chain of Log-Concave Markov Chainscited by 13
  23. 2021Multimeasurement Generative Modelscited by 8
  24. 2022On local entropy, stochastic control and deep neural networkscited by 7
  25. 2023Balanced Training of Energy-Based Models with Adaptive Flow Samplingcited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 11; 2025: 9; 2026: 7.

27 papers.

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  1. 2025No Trick, No Treat: Pursuits and Challenges Towards Simulation-free Training of Neural Samplerscited by 25
  2. 2024Training Neural Samplers with Reverse Diffusive KL Divergencecited by 21
  3. 2024Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusioncited by 19
  4. 2024BNEM: A Boltzmann Sampler Based on Bootstrapped Noised Energy Matchingcited by 14
  5. 2024Provable Convergence and Limitations of Geometric Tempering for Langevin Dynamicscited by 10
  6. 2025Microcanonical Langevin Ensembles: Advancing the Sampling of Bayesian Neural Networkscited by 10
  7. 2024Learned Reference-based Diffusion Sampling for multi-modal distributionscited by 9
  8. 2025Improving the evaluation of samplers on multi-modal targetscited by 9
  9. 2024Diffusion-PINN Samplercited by 7
  10. 2024Nonlinear Assimilation via Score-based Sequential Langevin Samplingcited by 7
  11. 2026Reverse Flow Matching: A Unified Framework for Online Reinforcement Learning with Diffusion and Flow Policiescited by 7
  12. 2024A Practical Diffusion Path for Samplingcited by 5
15 more
  1. 2024Sampling from multi-modal distributions with polynomial query complexity in fixed dimension via reverse diffusioncited by 4
  2. 2025End-To-End Learning of Gaussian Mixture Priors for Diffusion Samplercited by 4
  3. 2025Control Variate Score Matching for Diffusion Modelscited by 4
  4. 2025Joint stochastic localization and applicationscited by 2
  5. 2026Diffusion Path Samplers via Sequential Monte Carlocited by 2
  6. 2024Sequential transport maps using SoS density estimation and α-divergencescited by 1
  7. 2024New algorithms for sampling and diffusion modelscited by 1
  8. 2025Generative diffusion for perceptron problems: statistical physics analysis and efficient algorithmscited by 1
  9. 2025Sampling by averaging: A multiscale approach to score estimationcited by 1
  10. 2026Alternating Diffusion for Proximal Sampling with Zeroth Order Queriescited by 1
  11. 2026Exact Global MCMC with Denoising Diffusioncited by 1
  12. 2025Particle Monte Carlo methods for Lattice Field Theorycited by 0
  13. 2026Sampling via Stochastic Interpolants by Langevin-based Velocity and Initialization Estimation in Flow ODEscited by 0
  14. 2026Sampling from multi-modal distributions on Riemannian manifolds with training-free stochastic interpolantscited by 0
  15. 2026Total Variation Guarantees for Sampling with Stochastic Localizationcited by 0