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arXiv · 2609.37579

Ornstein-Uhlenbeck Is Hard to Beat, Yet Superlinear Drift Ships Lower Transport Costs

Attila Lovas·Lóránt Nagy
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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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Attila Lovas, Lóránt Nagy. 2026-09-29. Ornstein-Uhlenbeck Is Hard to Beat, Yet Superlinear Drift Ships Lower Transport Costs. https://arxiv.org/abs/2609.37579

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