mlsanityData to 14 Oct 2026

Langevin diffusions and the Metropolis-adjusted Langevin algorithm

arXiv 1309.2983 ↗First posted 11 Sep 2013stat.ME math.ST stat.THcited by 29

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Abstract (arXiv)

We provide a clarification of the description of Langevin diffusions on Riemannian manifolds and of the measure underlying the invariant density. As a result we propose a new position-dependent Metropolis-adjusted Langevin algorithm (MALA) based upon a Langevin diffusion in ℝd which has the required invariant density with respect to Lebesgue measure. We show that our diffusion and the diffusion upon which a previously-proposed position-dependent MALA is based are equivalent in some cases but are distinct in general. A simulation study illustrates the gain in efficiency provided by the new position-dependent MALA.

Key facts. Cited by 29 papers in the map (data through 14 Oct 2026). First posted on arXiv 11 Sep 2013.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 4; 2022: 4; 2023: 10; 2024: 6; 2025: 2; 2026: 3.

29 papers.

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  1. 2022Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisonscited by 170
  2. 2023A Comprehensive Survey on Knowledge Distillation of Diffusion Modelscited by 45
  3. 2022NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operatorscited by 33
  4. 2021Sampling with Mirrored Stein Operatorscited by 17
  5. 2023Optimal Preconditioning and Fisher Adaptive Langevin Samplingcited by 14
  6. 2023Entropy-based Training Methods for Scalable Neural Implicit Samplercited by 13
  7. 2022Lagrangian Manifold Monte Carlo on Monge Patchescited by 11
  8. 2023Normalizing flow sampling with Langevin dynamics in the latent spacecited by 7
  9. 2024Kinetic Interacting Particle Langevin Monte Carlocited by 7
  10. 2024Faster Sampling via Stochastic Gradient Proximal Samplercited by 5
  11. 2021A Unifying and Canonical Description of Measure-Preserving Diffusionscited by 4
  12. 2021Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamicscited by 4
17 more
  1. 2023ELF: Federated Langevin Algorithms with Primal, Dual and Bidirectional Compressioncited by 4
  2. 2023Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithmscited by 4
  3. 2023Warped geometric information on the optimisation of Euclidean functionscited by 3
  4. 2023AdamMCMC: Combining Metropolis Adjusted Langevin with Momentum-based Optimizationcited by 2
  5. 2023Transport map unadjusted Langevin algorithms: learning and discretizing perturbed samplerscited by 1
  6. 2021The Application of Zig-Zag Sampler in Sequential Markov Chain Monte Carlocited by 0
  7. 2022Clarifying MCMC-based training of modern EBMs : Contrastive Divergence versus Maximum Likelihoodcited by 0
  8. 2023Geometric Ergodicity in Modified Variations of Riemannian Manifold and Lagrangian Monte Carlocited by 0
  9. 2024An Improved Analysis of Langevin Algorithms with Prior Diffusion for Non-Log-Concave Samplingcited by 0
  10. 2024Robust Inference of Dynamic Covariance Using Wishart Processes and Sequential Monte Carlocited by 0
  11. 2024Feynman-Kac Operator Expectation Estimatorcited by 0
  12. 2024Denoising Fisher Training For Neural Implicit Samplerscited by 0
  13. 2025Backpropagation-Free Metropolis-Adjusted Langevin Algorithmcited by 0
  14. 2025Sampling on Metric Graphscited by 0
  15. 2026Time-Inhomogeneous Preconditioned Langevin Dynamicscited by 0
  16. 2026Gradient-free Riemannian Langevin Samplercited by 0
  17. 2026On skew-symmetric distributions and their use in Monte Carlo sampling algorithms: coordinate-free, Gibbs-style and manifold versions of the Barker proposalcited by 0