mlsanityData to 14 Oct 2026

Efficient Approximate Posterior Sampling with Annealed Langevin Monte Carlo

arXiv 2508.07631 ↗First posted 11 Aug 2025cs.LG cs.AI stat.MLcited by 3

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

We study the problem of posterior sampling in the context of score based generative models. We have a trained score network for a prior p(x), a measurement model p(y|x), and are tasked with sampling from the posterior p(x|y). Prior work has shown this to be intractable in KL (in the worst case) under well-accepted computational hardness assumptions. Despite this, popular algorithms for tasks such as image super-resolution, stylization, and reconstruction enjoy empirical success. Rather than establishing distributional assumptions or restricted settings under which exact posterior sampling is tractable, we view this as a more general "tilting" problem of biasing a distribution towards a measurement. Under minimal assumptions, we show that one can tractably sample from a distribution that is simultaneously close to the posterior of a noised prior in KL divergence and the true posterior in Fisher divergence. Intuitively, this combination ensures that the resulting sample is consistent with both the measurement and the prior. To the best of our knowledge these are the first formal results for (approximate) posterior sampling in polynomial time.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 28 of its 49 references that are in the map. First posted on arXiv 11 Aug 2025.

Builds on

28 of 49 references.

Closest ancestors · 8

Same direction, newest first

  1. 2025Non-asymptotic Analysis of Diffusion Annealed Langevin Monte Carlo for Generative Modelling13 Feb
  2. 2024Target Score Matching13 Feb
  3. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  4. 2022Convergence for score-based generative modeling with polynomial complexity13 Jun
  5. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  6. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  7. 2020Denoising Diffusion Implicit Models6 Oct
  8. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 20

  1. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,355
  2. 2021Zero-Shot Text-to-Image Generationcited by 4,288
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  4. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,430
  5. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,416
  6. 2022Denoising Diffusion Restoration Modelscited by 963
  7. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 521
  8. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 232
  9. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 227
  10. 2023Style Aligned Image Generation via Shared Attentioncited by 216
  11. 2024A Survey on Diffusion Models for Inverse Problemscited by 180
  12. 2024Semantic Image Inversion and Editing using Rectified Stochastic Differential Equationscited by 165
8 more
  1. 2018Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problemcited by 123
  2. 2023Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusioncited by 78
  3. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstructioncited by 73
  4. 2022Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlocited by 63
  5. 2024Provable Benefit of Annealed Langevin Monte Carlo for Non-log-concave Samplingcited by 23
  6. 2024Diffusion Posterior Sampling is Computationally Intractablecited by 20
  7. 2024Posterior Sampling with Denoising Oracles via Tilted Transportcited by 12
  8. 2025Mixing Time of the Proximal Sampler in Relative Fisher Information via Strong Data Processing Inequalitycited by 12

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Steering diffusion models with quadratic rewards: a fine-grained analysiscited by 5
  2. 2026Diffusion-Based Posterior Sampling: A Feynman-Kac Analysis of Bias and Stabilitycited by 2
  3. 2026The tractability landscape of diffusion alignment: regularization, rewards, and computational primitivescited by 2

Similar, not cited

Close in wording, no citation either way

  1. 2025Posterior Sampling by Combining Diffusion Models with Annealed Langevin Dynamics
  2. 2024Posterior sampling via Langevin dynamics based on generative priors
  3. 2022Score-Based Diffusion meets Annealed Importance Sampling
  4. 2025From Score Matching to Diffusion: A Fine-Grained Error Analysis in the Gaussian Setting
  5. 2026Latent Annealed Posterior Sampling with a Variance-Preserving Bridge for Sparsely Observed Random Fields
  6. 2023Preconditioned Score-based Generative Models
  7. 2025Preconditioned Langevin Dynamics with Score-Based Generative Models for Infinite-Dimensional Linear Bayesian Inverse Problems
  8. 2026A Stochastic Analysis Perspective on Diffusion Models