The paper introduces Hessian-free high-resolution (HFHR) dynamics, an extension of underdamped Langevin dynamics that incorporates reversible position diffusion for sampling in machine learning. It provides an explicit quantitative contraction rate under a position Poincaré inequality, weighted Hessian and Laplacian bounds, and a compact Sobolev embedding, even when the potential is non‑convex. For the HFHR Monte Carlo algorithm, a path‑space Girsanov argument yields a non‑asymptotic convergence bound and an explicit iteration complexity in total variation distance, improving on previous HFHR results and demonstrating benefits of a positive diffusion parameter through numerical experiments.
By Wujun Lv, Xiaoyu Wang, Yingli Wang, Lingjiong Zhu
arXiv:2608. 06283v1 Announce Type: new Abstract: We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex.
By Iosif Lytras, Nikolaos Makras, Sotirios Sabanis
We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex. We introduce the Subgradient Tamed Unadjusted Langevin Algorithm (SG-TULA), a discretisation of the Langevin diffusion that operates directly on subgradients, without relying on computationally demanding smoothing procedures.
arXiv:2609.40193v1 Announce Type: new
Abstract: We establish near-linear accuracy bounds for the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA). The target is $\pi\propto e^{-f-g}$, w...
By Yuchen Xin, Zhihua Zhang
arXiv:2609.06196v1 Announce Type: cross
Abstract: We study the computational effort required for global optimization of a smooth, possibly nonconvex objective $\Gamma:\mathbb{R}^d\to\mathbb{R}$. An a...
By Ioannis Kontoyiannis, Sean Meyn
The paper introduces penalized nonreversible Langevin algorithms for sampling from a target distribution constrained to a compact convex set. It combines a squared distance penalty with skew-symmetric perturbations that preserve the penalized Gibbs distribution, and provides nonasymptotic total variation and Wasserstein bounds under various smoothness and contraction assumptions. Numerical experiments demonstrate the methods on constrained Bayesian regression, classification, neural networks, and truncated sampling, highlighting acceleration in a stochastic quadratic model.
By Pervez Ali, Weihao Dong, Xiaoyu Wang
arXiv:2407.05790v4 Announce Type: replace-cross
Abstract: This paper introduces and analyses interacting underdamped Langevin algorithms, termed Kinetic Interacting Particle Langevin Monte Carlo (KIP...
By Paul Felix Valsecchi Oliva, O. Deniz Akyildiz
arXiv:2602. 15008v2 Announce Type: replace Abstract: Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete.
By Daniil Dmitriev, Zhihan Huang, Yuting Wei
The paper proves that for discrete diffusion models using uniform or remasking forward processes, an adaptive sampler based on a leave‑one‑out denoiser can achieve sampling error proportional to the score‑estimation error plus a small tolerance. The required number of discretization steps scales with the dual total correlation of the target distribution, not directly with the ambient dimension. This result shows that sampling complexity is governed by the intrinsic dependence structure of the distribution, and the authors provide an information‑theoretic analysis linking discretization error to mutual information between coordinates.
By Daniil Dmitriev, Zhihan Huang, Yuting Wei
arXiv:2607. 15208v1 Announce Type: cross Abstract: Unadjusted samplers such as unadjusted Hamiltonian Monte Carlo and underdamped Langevin are well-known to be biased.
By Yifan Chen, Xiaoou Cheng, Jonathan Niles-Weed, Jonathan Weare
arXiv:2610. 12052v1 Announce Type: cross Abstract: Despite their empirical success, why diffusion models overcome the bottlenecks of classical score-based samplers remains unclear.
By Adam Perbost, Francis Bach, Pierre Marion
The paper introduces a new underdamped Langevin system for sampling Gibbs distributions on matrix spaces where the potential energy is neither convex nor globally gradient‑Lipschitz. By employing non‑quadratic kinetic energies, the authors achieve momentum preconditioning that smooths the momentum via a spectral taming of its gradient. They prove that this dynamics preserves the target Gibbs measure, converges exponentially fast in a weighted total variation distance, and that its Euler–Maruyama discretization remains stable with uniform moment bounds over time.
By Nikolaos Makras, Sotirios Sabanis