Dimension-Free Multimodal Sampling via Preconditioned Annealed Langevin Dynamics

• URL: http://arxiv.org/abs/2602.01449v1
• Date: Sun, 01 Feb 2026 21:37:33 GMT
• Title: Dimension-Free Multimodal Sampling via Preconditioned Annealed Langevin Dynamics
• Authors: Lorenzo Baldassari, Josselin Garnier, Knut Solna, Maarten V. de Hoop,
• Abstract summary: Annealed Langevin dynamics (ALD) is a widely used alternative to classical Langevin since it often yields much faster mixing on multimodal targets.<n>We help bridge this gap by providing a uniform-in-dimension analysis of continuous-time ALD for multimodal targets.
• Score: 10.631439631816166
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Designing algorithms that can explore multimodal target distributions accurately across successive refinements of an underlying high-dimensional problem is a central challenge in sampling. Annealed Langevin dynamics (ALD) is a widely used alternative to classical Langevin since it often yields much faster mixing on multimodal targets, but there is still a gap between this empirical success and existing theory: when, and under which design choices, can ALD be guaranteed to remain stable as dimension increases? In this paper, we help bridge this gap by providing a uniform-in-dimension analysis of continuous-time ALD for multimodal targets that can be well-approximated by Gaussian mixture models. Along an explicit annealing path obtained by progressively removing Gaussian smoothing of the target, we identify sufficient spectral conditions - linking smoothing covariance and the covariances of the Gaussian components of the mixture - under which ALD achieves a prescribed accuracy within a single, dimension-uniform time horizon. We then establish dimension-robustness to imperfect initialization and score approximation: under a misspecified-mixture score model, we derive explicit conditions showing that preconditioning the ALD algorithm with a sufficiently decaying spectrum is necessary to prevent error terms from accumulating across coordinates and destroying dimension-uniform control. Finally, numerical experiments illustrate and validate the theory.

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