The paper proves quantitative convergence to the target distribution and uniform‑in‑time propagation of chaos for Langevin‑regularized Stein variational gradient descent (SVGD). It shows that both the Stein interaction and the Langevin drift dissipate the same relative entropy, yielding exponential convergence under a log‑Sobolev inequality and providing finite‑particle entropy identities for empirical measures. Two finite‑time approaches—synchronous coupling and moving‑product entropy—are developed to give explicit Wasserstein, kernel Stein discrepancy, and total variation bounds, leading to polynomial uniform‑in‑time propagation of chaos rates.
By Sayan Banerjee, Dohyeon Kim
arXiv:2610.02081v1 Announce Type: new
Abstract: There has been a proliferation of sampling algorithms based on Wasserstein gradient flows (WGF) and forward-only diffusion processes (FODP), often acco...
By Daniel McBride, Pratik Khandagale, Cristina Garcia-Cardona, Yen Ting Lin
The paper presents a new one‑step generative modeling framework for finite state spaces, leveraging discrete Wasserstein geometry to define a target‑relative KL gradient flow over a reversible Markov kernel. The authors implement this flow at the particle level using Markov jumps and encode the resulting transport updates into a latent‑conditioned generator, enabling one‑step inference after training. Experiments on a controlled setting confirm KL dissipation, consistency between particle dynamics and probability flow, and accurate numerical scaling, while a finite‑capacity neural generator successfully tracks the exact transport targets.
By Alessandro Micheli, Andrea Zerio, Samir Bhatt
arXiv:2606. 07325v1 Announce Type: cross Abstract: We study the minimax rate of estimating a future value $\mu_{t_n+h}$ of a curve $t\mapsto\mu_t$ in the $2$-Wasserstein space $\mathcal{P}_2(\mathbb{R}^d)$ from finitely many noisy snapshots of its past, under an adiabatic bound $\|\nabla_t^k v\|\le\varepsilon$ on the $k$-th covariant derivative of the velocity field.
By Munsik Kim
arXiv:2610. 19773v1 Announce Type: new Abstract: Score-based generative models driven by $\alpha$-stable L{\'e}vy processes have been proposed as an alternative to Brownian diffusion models, with empirical evidence suggesting improved sampling and better modeling of heavy-tailed data.
By Ianis Hammani (ENS Paris Saclay, LMO), Claire Boyer (LMO, IUF)
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
The paper studies the finite‑sample approximation of a Hessian‑guided perturbed Wasserstein gradient flow (PWGF), which adds Gaussian perturbations to Wasserstein gradient descent to escape saddle points in nonconvex problems. It analyzes when an interacting‑particle approximation remains accurate over growing time horizons, showing that accumulated negative curvature can amplify errors while subsequent positive curvature can damp them. Under regularity assumptions and a fixed perturbation schedule, the authors prove high‑probability tracking bounds for both particles and objective values, construct a population‑first coupling to handle state‑dependent jumps, and verify the theory in a variance‑plus‑cosine model and a regularized matrix‑factorization setting.
By Ryotaro Kawata, Atsushi Nitanda, Taiji Suzuki
arXiv:2409. 08469v4 Announce Type: replace-cross Abstract: We provide finite-particle convergence rates for the Stein Variational Gradient Descent (SVGD) algorithm in the Kernelized Stein Discrepancy ($\mathsf{KSD}$) and Wasserstein-2 metrics.
By Sayan Banerjee, Krishnakumar Balasubramanian, Promit Ghosal
arXiv:2610.19861v1 Announce Type: cross
Abstract: We study the optimisation landscape of the maximum mean discrepancy (MMD) over weighted atomic measures. For the one-dimensional Gaussian kernel, we...
By Tharrshann Jayan Logarajah, Jeremias Knoblauch, Louis Sharrock
arXiv:2607. 04738v1 Announce Type: cross Abstract: Reconstructing population dynamics is a central problem in the physical and data sciences.
By Markus Heinonen, Yair Shenfeld, Ricardo Baptista, Daniel Waxman, Dmitry Batenkov, Tim Cooijmans, Eli Bingham
arXiv:2610.19878v1 Announce Type: new
Abstract: Population dynamics are often observed only as unpaired snapshots, which leave the evolution between measurements underdetermined. Second-order regular...
By Amartya Banerjee, Harlin Lee, Caroline Moosm\"uller
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.