Uniform-in-time propagation-of-chaos bounds for SVGD are obtained via cutoff for distributional metrics (logarithmic rates) and via finite-dimensional closure plus conjugacy for Gaussian targets (parametric N^{-1/2} rates).
On the Wasserstein Gradient Flow Interpretation of Drifting Models
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Recently, Deng et al. (2026) proposed Generative Modeling via Drifting (GMD), a novel framework for generative tasks. This note presents an analysis of GMD through the lens of Wasserstein Gradient Flows (WGF), i.e., the path of steepest descent for a functional in the space of probability measures, equipped with the geometry of optimal transport. Unlike previous WGF-based contributions, GMD can be thought of as directly targeting a fixed point of a specific WGF flow. We demonstrate three main results: first, that one algorithm proposed by Deng et al. (2026) corresponds to finding the limiting point of a WGF on the KL divergence, with Parzen smoothing on the densities. Second, that the algorithm actually implemented by Deng et al. (2026) corresponds to a different procedure, which bears some resemblance to the fixed point of a WGF on the Sinkhorn divergence, but lacks certain desirable properties of the latter. Third, the same same idea can be extended to the limiting point of other WGFs, including the Maximum Mean Discrepancy (MMD), the sliced Wasserstein distance, and GAN critic functions.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Derives continuous-time finite-particle convergence rates for a new conservative KDE-gradient drifting method and the non-conservative Laplace kernel method in one-step generative modeling.
citing papers explorer
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Uniform-in-time Propagation-of-Chaos for Stein Variational Gradient Descent
Uniform-in-time propagation-of-chaos bounds for SVGD are obtained via cutoff for distributional metrics (logarithmic rates) and via finite-dimensional closure plus conjugacy for Gaussian targets (parametric N^{-1/2} rates).
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Finite-Particle Convergence Rates for Conservative and Non-Conservative Drifting Models
Derives continuous-time finite-particle convergence rates for a new conservative KDE-gradient drifting method and the non-conservative Laplace kernel method in one-step generative modeling.