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Tag: langevin

  • Anchored Langevin Algorithms

    Anchored Langevin Algorithms arXiv:2509.19455v1 Announce Type: new Abstract: Standard first-order Langevin algorithms such as the unadjusted Langevin algorithm (ULA) are obtained by discretizing the Langevin diffusion and are widely used for sampling in machine learning because they scale to high dimensions and large datasets. However, they face two key limitations: (i) they require differentiable log-densities,…

  • Underdamped Langevin MCMC with third order convergence

    Underdamped Langevin MCMC with third order convergence arXiv:2508.16485v1 Announce Type: new Abstract: In this paper, we propose a new numerical method for the underdamped Langevin diffusion (ULD) and present a non-asymptotic analysis of its sampling error in the 2-Wasserstein distance when the $d$-dimensional target distribution $p(x)propto e^{-f(x)}$ is strongly log-concave and has varying degrees of…

  • Critically-Damped Higher-Order Langevin Dynamics

    Critically-Damped Higher-Order Langevin Dynamics arXiv:2506.21741v1 Announce Type: new Abstract: Denoising Diffusion Probabilistic Models represent an entirely new class of generative AI methods that have yet to be fully explored. Critical damping has been successfully introduced in Critically-Damped Langevin Dynamics (CLD) and Critically-Damped Third-Order Langevin Dynamics (TOLD++), but has not yet been applied to dynamics of…

  • Non-asymptotic Analysis of Diffusion Annealed Langevin Monte Carlo for Generative Modelling

    Non-asymptotic Analysis of Diffusion Annealed Langevin Monte Carlo for Generative Modelling arXiv:2502.09306v1 Announce Type: new Abstract: We investigate the theoretical properties of general diffusion (interpolation) paths and their Langevin Monte Carlo implementation, referred to as diffusion annealed Langevin Monte Carlo (DALMC), under weak conditions on the data distribution. Specifically, we analyse and provide non-asymptotic error…

  • Preconditioned Subspace Langevin Monte Carlo

    Preconditioned Subspace Langevin Monte Carlo arXiv:2412.13928v1 Announce Type: new Abstract: We develop a new efficient method for high-dimensional sampling called Subspace Langevin Monte Carlo. The primary application of these methods is to efficiently implement Preconditioned Langevin Monte Carlo. To demonstrate the usefulness of this new method, we extend ideas from subspace descent methods in Euclidean…

  • Langevin Monte Carlo Beyond Lipschitz Gradient Continuity

    Langevin Monte Carlo Beyond Lipschitz Gradient Continuity arXiv:2412.09698v1 Announce Type: new Abstract: We present a significant advancement in the field of Langevin Monte Carlo (LMC) methods by introducing the Inexact Proximal Langevin Algorithm (IPLA). This novel algorithm broadens the scope of problems that LMC can effectively address while maintaining controlled computational costs. IPLA extends LMC’s…