PreprintCC BY 4.0arXiv
Ornstein-Uhlenbeck Is Hard to Beat, Yet Superlinear Drift Ships Lower Transport Costs
Abstract
Brešar and Mijatović \cite{bresar2025} show that Ornstein--Uhlenbeck diffusion is hard to beat in forward convergence under assumptions that exclude superlinear drift. We instead test superlinear Langevin diffusions for score-based image generation, computing their conditional scores numerically from a Fokker--Planck equation. In our experiments, the superlinear models beat the Ornstein--Uhlenbeck baseline on empirical Wasserstein distance across nearly the entire tested grid and show less variation across diffusion horizons. The ``hard to beat'' verdict of \cite{bresar2025} thus fails to be universal.
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BibTeX
@misc{lovas2026ornsteinuhlenbeck,
title = {{Ornstein-Uhlenbeck Is Hard to Beat, Yet Superlinear Drift Ships Lower Transport Costs}},
author = {Attila Lovas and Lóránt Nagy},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37579},
eprint = {2609.37579},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37579},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Ornstein-Uhlenbeck Is Hard to Beat, Yet Superlinear Drift Ships Lower Transport Costs
AU - Attila Lovas
AU - Lóránt Nagy
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37579
UR - https://arxiv.org/abs/2609.37579
AB - Brešar and Mijatović \cite{bresar2025} show that Ornstein--Uhlenbeck diffusion is hard to beat in forward convergence under assumptions that exclude superlinear drift. We instead test superlinear Langevin diffusions for score-based image generation, computing their conditional scores numerically from a Fokker--Planck equation. In our experiments, the superlinear models beat the Ornstein--Uhlenbeck baseline on empirical Wasserstein distance across nearly the entire tested grid and show less variation across diffusion horizons. The ``hard to beat'' verdict of \cite{bresar2025} thus fails to be universal.
ER -