Published on May 19, 2026
Researchers have identified significant challenges in obtaining stable diffusion-based samplers, particularly in high-dimensional settings. Conventional methods often lead to accumulated errors, undermining stability when refining finite-dimensional approximations. This issue is prevalent in the context of multimodal Gaussian mixtures.
A recent paper introduces a method that leverages preconditioned annealed Langevin dynamics (ALD) to address these instability problems. The authors demonstrate that using Euler-Maruyama (EM) discretization can impose stability constraints that impact the preconditioner and covariance scale. This relationship is crucial for ensuring that the initial smoothed law closely aligns with the target across varying dimensions.
The study reveals that an exponential-integrator scheme can better handle the stiff linear components of the annealed score. spectral summability conditions, the researchers prove a dimension-uniform Kullback-Leibler bound for this improved scheme. Their results suggest that allowing adequate time for annealing significantly reduces divergence in the KL measure, adapting well to dimensional increases.
This work presents valuable insights for researchers seeking reliable sampling techniques in high-dimensional scenarios. The findings not only clarify the scheme-dependent nature of previous constraints but also provide a framework for minimizing error accumulation. This advancement could lead to more effective applications in various fields dealing with complex probabilistic models.
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