Ornstein-Uhlenbeck Is Hard to Beat, Yet Superlinear Drift Ships Lower Transport Costs
stat.ML, cs.LG
Submitted: 2026-09-29
Updated: 2026-09-29
Code: https://github.com/lorant-nagy/genai
License: http://creativecommons.org/licenses/by/4.0/
The gist: Brešar and Mijatović show that Ornstein--Uhlenbeck diffusion is hard to beat in forward convergence under assumptions that exclude superlinear drift.
Terminology
Abstract
Brešar and Mijatović 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 thus fails to be universal.
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