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Langevin dynamics sampling suffers from extremely low generation speed, fundamentally limited by numerous fine-grained iterations to converge to the target distribution. We introduce PID-controlled Langevin Dynamics (PIDLD), a novel…

Machine Learning · Computer Science 2025-11-18 Hongyi Chen , Jianhai Shu , Jingtao Ding , Yong Li , Xiao-Ping Zhang

Score-based diffusion methods provide a powerful strategy to solve image restoration tasks by flexibly combining a pre-trained foundational prior model with a likelihood function specified during test time. Such methods are predominantly…

Computer Vision and Pattern Recognition · Computer Science 2024-09-09 Charlesquin Kemajou Mbakam , Jean-Francois Giovannelli , Marcelo Pereyra

Sampling from distributions play a crucial role in aiding practitioners with statistical inference. However, in numerous situations, obtaining exact samples from complex distributions is infeasible. Consequently, researchers often turn to…

Computation · Statistics 2024-04-01 Riddhiman Bhattacharya , Tiefeng Jiang

In this work we study the diffusion annealed Langevin dynamics, a score-based diffusion process recently introduced in the theory of generative models and which is an alternative to the classical overdamped Langevin diffusion. Our goal is…

Probability · Mathematics 2025-11-14 Patrick Cattiaux , Paula Cordero-Encinar , Arnaud Guillin

Sampling from a target distribution is a fundamental problem. Traditional Markov chain Monte Carlo (MCMC) algorithms, such as the unadjusted Langevin algorithm (ULA), derived from the overdamped Langevin dynamics, have been extensively…

Optimization and Control · Mathematics 2024-10-29 Xinzhe Zuo , Stanley Osher , Wuchen Li

For sampling from a log-concave density, we study implicit integrators resulting from $\theta$-method discretization of the overdamped Langevin diffusion stochastic differential equation. Theoretical and algorithmic properties of the…

Machine Learning · Statistics 2021-07-13 Liam Hodgkinson , Robert Salomone , Fred Roosta

This work introduces a sampling method capable of solving Bayesian inverse problems in function space. It does not assume the log-concavity of the likelihood, meaning that it is compatible with nonlinear inverse problems. The method…

Machine Learning · Statistics 2024-05-27 Lorenzo Baldassari , Ali Siahkoohi , Josselin Garnier , Knut Solna , Maarten V. de Hoop

We consider a family of unadjusted generalized HMC samplers, which includes standard position HMC samplers and discretizations of the underdamped Langevin process. A detailed analysis and optimization of the parameters is conducted in the…

Probability · Mathematics 2024-05-24 Nicolaï Gouraud , Pierre Le Bris , Adrien Majka , Pierre Monmarché

We study Langevin dynamics with a kinetic energy different from the standard, quadratic one in order to accelerate the sampling of Boltzmann-Gibbs distributions. In particular, this kinetic energy can be non-globally Lipschitz, which raises…

Statistical Mechanics · Physics 2018-05-15 Gabriel Stoltz , Zofia Trstanova

In this paper we introduce and analyse Langevin samplers that consist of perturbations of the standard underdamped Langevin dynamics. The perturbed dynamics is such that its invariant measure is the same as that of the unperturbed dynamics.…

Probability · Mathematics 2017-12-06 A. B. Duncan , N. Nuesken , G. A. Pavliotis

We investigate the Cahn-Hilliard equation with nonlinear diffusion and non-degenerate mobility modeling phase separation phenomena in complex systems (e.g., crystals and polymers). Previous results in the literature on this model relied on…

Analysis of PDEs · Mathematics 2025-10-10 Monica Conti , Stefania Gatti , Andrea Giorgini , Giulio Schimperna

Langevin diffusion is a commonly used tool for sampling from a given distribution. In this work, we establish that when the target density $p^*$ is such that $\log p^*$ is $L$ smooth and $m$ strongly convex, discrete Langevin diffusion…

Machine Learning · Statistics 2017-11-02 Xiang Cheng , Peter Bartlett

We propose a sampling method based on an ensemble approximation of second order Langevin dynamics. The log target density is appended with a quadratic term in an auxiliary momentum variable and damped-driven Hamiltonian dynamics introduced;…

Dynamical Systems · Mathematics 2025-06-06 Ziming Liu , Andrew M. Stuart , Yixuan Wang

We propose efficient Langevin Monte Carlo algorithms for sampling distributions with nonsmooth convex composite potentials, which is the sum of a continuously differentiable function and a possibly nonsmooth function. We devise such…

Machine Learning · Statistics 2022-07-12 Tim Tsz-Kit Lau , Han Liu

We study Langevin-type algorithms for sampling from Gibbs distributions such that the potentials are dissipative and their weak gradients have finite moduli of continuity not necessarily convergent to zero. Our main result is a…

Statistics Theory · Mathematics 2024-03-01 Shogo Nakakita

We present a novel method for drawing samples from Gibbs distributions with densities of the form $\pi(x) \propto \exp(-U(x))$. The method accelerates the unadjusted Langevin algorithm by introducing an inertia term similar to Polyak's…

Numerical Analysis · Mathematics 2025-10-09 Alexander Falk , Andreas Habring , Christoph Griesbacher , Thomas Pock

We propose discrete Langevin proposal (DLP), a simple and scalable gradient-based proposal for sampling complex high-dimensional discrete distributions. In contrast to Gibbs sampling-based methods, DLP is able to update all coordinates in…

Machine Learning · Computer Science 2022-06-22 Ruqi Zhang , Xingchao Liu , Qiang Liu

Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…

Computation · Statistics 2016-12-06 Arnak S. Dalalyan

An effective approach for sampling from unnormalized densities is based on the idea of gradually transporting samples from an easy prior to the complicated target distribution. Two popular methods are (1) Sequential Monte Carlo (SMC), where…

Machine Learning · Statistics 2025-09-09 Junhua Chen , Lorenz Richter , Julius Berner , Denis Blessing , Gerhard Neumann , Anima Anandkumar

In this work, we propose a first-order sampling method called the Metropolis-adjusted Preconditioned Langevin Algorithm for approximate sampling from a target distribution whose support is a proper convex subset of $\mathbb{R}^{d}$. Our…

Computation · Statistics 2025-02-27 Vishwak Srinivasan , Andre Wibisono , Ashia Wilson