mlsanityData to 14 Oct 2026

High-Order Langevin Diffusion Yields an Accelerated MCMC Algorithm

arXiv 1908.10859 ↗First posted 28 Aug 2019stat.ML cs.DS cs.LGcited by 36

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Abstract (arXiv)

We propose a Markov chain Monte Carlo (MCMC) algorithm based on third-order Langevin dynamics for sampling from distributions with log-concave and smooth densities. The higher-order dynamics allow for more flexible discretization schemes, and we develop a specific method that combines splitting with more accurate integration. For a broad class of d-dimensional distributions arising from generalized linear models, we prove that the resulting third-order algorithm produces samples from a distribution that is at most varepsilon > 0 in Wasserstein distance from the target distribution in Oleft(fracd1/4 varepsilon1/2 right) steps. This result requires only Lipschitz conditions on the gradient. For general strongly convex potentials with α-th order smoothness, we prove that the mixing time scales as O left(fracd1/4varepsilon1/2 + fracd1/2varepsilon1/(α - 1) right).

Key facts. Cited by 36 papers in the map (data through 14 Oct 2026). First posted on arXiv 28 Aug 2019.

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Citing papers per year: 2021: 11; 2022: 3; 2023: 10; 2024: 4; 2025: 6; 2026: 2.

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  1. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusioncited by 233
  2. 2021Estimating High Order Gradients of the Data Distribution by Denoisingcited by 64
  3. 2022Private Convex Optimization via Exponential Mechanismcited by 49
  4. 2025Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithmscited by 47
  5. 2021Minimax Mixing Time of the Metropolis-Adjusted Langevin Algorithm for Log-Concave Samplingcited by 44
  6. 2023Reverse Diffusion Monte Carlocited by 41
  7. 2023On the Posterior Distribution in Denoising: Application to Uncertainty Quantificationcited by 33
  8. 2023Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusionscited by 29
  9. 2025Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distancecited by 29
  10. 2025Underdamped Diffusion Bridges with Applications to Samplingcited by 29
  11. 2021Sqrt(d) Dimension Dependence of Langevin Monte Carlocited by 25
  12. 2021Lower Bounds on Metropolized Sampling Methods for Well-Conditioned Distributionscited by 19
24 more
  1. 2021Heavy-tailed denoising score matchingcited by 18
  2. 2023A connection between Tempering and Entropic Mirror Descentcited by 16
  3. 2023When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?cited by 15
  4. 2021On Convergence of Federated Averaging Langevin Dynamicscited by 14
  5. 2023Chain of Log-Concave Markov Chainscited by 14
  6. 2021When is the Convergence Time of Langevin Algorithms Dimension Independent? A Composite Optimization Viewpointcited by 12
  7. 2023Langevin Monte Carlo for strongly log-concave distributions: Randomized midpoint revisitedcited by 10
  8. 2021Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equationscited by 8
  9. 2022Hamiltonian Monte Carlo for efficient Gaussian sampling: long and random stepscited by 8
  10. 2023Solving Linear Inverse Problems using Higher-Order Annealed Langevin Diffusioncited by 6
  11. 2024Parallel Simulation for Log-concave Sampling and Score-based Diffusion Modelscited by 6
  12. 2024Generative Modelling with High-Order Langevin Dynamicscited by 5
  13. 2024Faster Sampling via Stochastic Gradient Proximal Samplercited by 5
  14. 2025Sequential Monte Carlo approximations of Wasserstein--Fisher--Rao gradient flowscited by 5
  15. 2023Accelerated Bayesian imaging by relaxed proximal-point Langevin samplingcited by 4
  16. 2025Accelerating Langevin Monte Carlo Sampling: A Large Deviations Analysiscited by 4
  17. 2021De-randomizing MCMC dynamics with the diffusion Stein operatorcited by 3
  18. 2022Learning and Inference in Sparse Coding Models with Langevin Dynamicscited by 2
  19. 2025An operator splitting analysis of Wasserstein--Fisher--Rao gradient flowscited by 2
  20. 2026Improved Guarantees for Langevin Monte Carlo with Average Smoothnesscited by 2
  21. 2021Quantifying the mini-batching error in Bayesian inference for Adaptive Langevin dynamicscited by 1
  22. 2023A Gentle Introduction to Gradient-Based Optimization and Variational Inequalities for Machine Learningcited by 0
  23. 2024Feynman-Kac Operator Expectation Estimatorcited by 0
  24. 2026Particle-based Generalised Stochastic Optimisationcited by 0