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arXiv Machine Learning By Stefano Goria, Levent A. Meng\"ut\"urk, Murat C. Meng\"ut\"urk, Berkan Sesen

Random-Bridges as Stochastic Transports for Generative Models

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This paper introduces random-bridges—stochastic processes conditioned to hit target distributions at fixed times—as stochastic transports for generative modeling. Random-bridges can be Markovian or non‑Markovian, continuous or discontinuous, depending on the driving process, and the authors develop both theoretical foundations and practical training/simulation algorithms for Gaussian and Lévy (Gamma, Poisson, Stable‑1/2) bridges. Empirical results on the Gaussian case show that the proposed framework produces high‑quality samples with competitive Fréchet Inception Distance scores relative to popular denoising diffusion and flow‑matching methods.

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