mlsanityData to 14 Oct 2026

Dimension-Uniform Discretization Analysis of Preconditioned Annealed Langevin Dynamics for Multimodal Gaussian Mixtures

arXiv 2605.16473 ↗First posted 15 May 2026stat.ML cs.LG cs.NAcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Obtaining stable diffusion-based samplers in high- and infinite-dimensional settings is challenging because errors can accumulate across high-frequency coordinates and make the dynamics unstable under refinement of the finite-dimensional approximation of the underlying function-space problem. Discretization is a typical source of such errors, and preconditioning with a suitable spectral decay is one way to control their accumulation. In this paper, we study this problem for preconditioned annealed Langevin dynamics (ALD) applied to Gaussian mixtures. We first show that Euler-Maruyama (EM) discretization, by treating the stiff linear part of the annealed score with a forward Euler step, imposes a stability constraint coupling the preconditioner with the annealed covariance scale. Together with the conditions ensuring dimension-uniform control of the annealed dynamics, this constraint forces the initial smoothed law to remain uniformly close to the target across dimensions. We then consider an exponential-integrator scheme that integrates the stiff linear part of the annealed score exactly. Under explicit spectral summability conditions coupling the smoothing covariance, the component covariance spectra, and the preconditioner, we prove a dimension-uniform Kullback-Leibler (KL) bound for this scheme. This bound can be made arbitrarily small, uniformly in dimension, by allowing enough time for annealing and then refining the time mesh accordingly. Importantly, these conditions allow regimes in which the KL divergence between the target and the initial smoothed law diverges with dimension, showing that the restrictions imposed by EM are scheme-dependent rather than intrinsic to ALD.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 23 of its 52 references that are in the map. First posted on arXiv 15 May 2026.

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23 of 52 references.

Closest ancestors · 11

Same direction, newest first

  1. 2025Preconditioned Langevin Dynamics with Score-Based Generative Models for Infinite-Dimensional Linear Bayesian Inverse Problems23 May
  2. 2025Non-asymptotic Analysis of Diffusion Annealed Langevin Monte Carlo for Generative Modelling13 Feb
  3. 2023∞-Diff: Infinite Resolution Diffusion with Subsampled Mollified States31 Mar
  4. 2023Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generation8 Mar
  5. 2023Continuous-Time Functional Diffusion Processes1 Mar
  6. 2023Infinite-Dimensional Diffusion Models20 Feb
  7. 2023Score-based Diffusion Models in Function Space14 Feb
  8. 2022Diffusion Generative Models in Infinite Dimensions1 Dec
  9. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  10. 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
  11. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 12

  1. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  2. 2018Sampling Can Be Faster Than Optimizationcited by 68
  3. 2023Conditional score-based diffusion models for Bayesian inference in infinite dimensionscited by 38
  4. 2014Dimension-independent likelihood-informed MCMCcited by 37
  5. 2024Provable Benefit of Annealed Langevin Monte Carlo for Non-log-concave Samplingcited by 23
  6. 2022Annealed Langevin Dynamics for Massive MIMO Detectioncited by 16
  7. 2024Provable Convergence and Limitations of Geometric Tempering for Langevin Dynamicscited by 10
  8. 2016Improving the convergence of reversible samplerscited by 8
  9. 2024Taming Score-Based Diffusion Priors for Infinite-Dimensional Nonlinear Inverse Problemscited by 7
  10. 2023Solving Linear Inverse Problems using Higher-Order Annealed Langevin Diffusioncited by 6
  11. 2025Diffusion annealed Langevin dynamics: a theoretical studycited by 4
  12. 2026Dimension-Free Multimodal Sampling via Preconditioned Annealed Langevin Dynamicscited by 3

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