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Preprint Aug 2026

Weighted Laplacian Flow: A Deterministic Particle Flow with Exponential Convergence

We introduce weighted Laplacian flow (WLF), a deterministic particle-flow framework for sampling from a target distribution known only up to normalization. The proposed method evolves the logarithmic density ratio through a transport equation and determines the particle velocity from a target-weighted Poisson problem,...

Wei-Ye Gan, Tang-Jun Wang, Zuo-Qiang Shi · 0 citations
Preprint Aug 2026

Diffusion Quasi-Monte Carlo

This work constructs a cube-to-target map by composing a Gaussian base transformation (the component-wise inverse Gaussian CDF) with an Euler-discretized probability flow ODE, and establishes conditions for diffusion probability-flow transport under mild bounded-derivative assumptions on the learned vector field.

Jian-Long Chen, Yi-Feng Yu · 0 citations
Preprint Aug 2026

Ordered Diffusion Kernels

We introduce Ordered Diffusion Kernels (ODKs), a novel class of local kernels that can approximate the infinitesimal generator of an arbitrary It\^o Stochastic Differential Equation (SDE). ODKs are designed to be applied to data sampled from dynamical systems where little dynamical information is available a priori. Th...

Jack H. Soulsby, A. C. S. Jørgensen, Atiyo Ghosh et al. · 0 citations
Preprint Aug 2026

Convergence of time-discrete finite particle consensus based optimization in Hilbert spaces

This analysis provides convergence guarantees directly for the computable particle system, complementing recent continuous-time and mean-field results in infinite dimensions and establishing quantitative pairwise contraction, exponential decay of the expected swarm variance, and almost-sure convergence of all particles...

Michael Herty, Hui Huang, Hicham Kouhkouh · 0 citations
Preprint Oct 2026

Deterministic and stochastic particle methods for the Fokker-Planck equation in S--formulation with application to point set registration

We present two particle methods for point set registration in bounded domains based on the Fokker-Planck equation. The first method relies on a moving least squares discretization of the S--formulation, in which moving grid points (particles) are advected by the drift with the target distribution, diffusion is resolved...

Klaas Willems, A. Iollo, G. Russo et al. · 0 citations

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