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.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2609.37579 [stat.ML]

(or arXiv:2609.37579v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2609.37579 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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