{"ID":2835139,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.00386","arxiv_id":"2512.00386","title":"Convergence of Reflected Langevin Diffusion for Constrained Sampling","abstract":"We examine the Langevin diffusion confined to a closed, convex domain $D\\subset\\mathbb{R}^d$, represented as a reflected stochastic differential equation. We introduce a sequence of penalized stochastic differential equations and prove that their invariant measures converge, in Wasserstein-2 distance and with explicit polynomial rate, to the invariant measure of the reflected Langevin diffusion. We also analyze a time-discretization of the penalized process obtained via the Euler-Maruyama scheme and demonstrate the convergence to the original constrained measure. These results provide a rigorous approximation framework for reflected Langevin dynamics in both continuous and discrete time.","short_abstract":"We examine the Langevin diffusion confined to a closed, convex domain $D\\subset\\mathbb{R}^d$, represented as a reflected stochastic differential equation. We introduce a sequence of penalized stochastic differential equations and prove that their invariant measures converge, in Wasserstein-2 distance and with explicit...","url_abs":"https://arxiv.org/abs/2512.00386","url_pdf":"https://arxiv.org/pdf/2512.00386v2","authors":"[\"Tarika Mane\",\"Amine Boukardagha\"]","published":"2025-11-29T08:24:03Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.ST\"]","methods":"[\"Diffusion Model\"]","has_code":false}