Year: 2026
Type: preprint
Abstract: Current conditioned generative models heavily rely on score functions for guidance during training. When the generative model is a diffusion process with a singular diffusion coefficient and the underlying (conditional) densities either do not exist or are not smooth, we use causal optimal transport to define \emph{approximate} loss functions that identify a minimum-entropy control for guidance under minimal assumptions. Our approach relies on causal optimal transport and its characterization through the predictable representation property of (conditioned) diffusion processes whose associated martingale problem is well posed, à la Üstünel.
Source: arXiv (Cornell University)
Authors: Aydın, Uğur, Başar, Tamer
Institution: University of Illinois Urbana-Champaign
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1523888516, G7506262489
OpenAlex ID: W7208769041
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