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This arXiv paper proposes random-bridge stochastic processes, conditioned to hit target distributions at fixed times, as a generative modelling framework, with Gaussian and Lévy-driven variants. Its empirical evidence is limited to Gaussian cases, where it reports Fréchet Inception Distance scores competitive with diffusion and flow-matching baselines, so the practical advantage over established methods remains to be shown. For ML researchers, the contribution is mainly a theoretical unification of generative transports that could open routes to non-Gaussian, jump-based generative models.
Random-Bridges as Stochastic Transports for Generative Models
arXiv:2512.14190v4 Announce Type: replace Abstract: This paper motivates the use of random-bridges -- stochastic processes conditioned to take target distributions at fixed timepoints -- in the realm of generative modelling. Herein, random-bridges act as stochastic transports between two probability distributions when appropriately initialized, displaying either Markovian or non-Markovian, and continuous, discontinuous, or hybrid patterns depending on the choice of the driving process. We show how one can start from general probabilistic statements and branch out into specific representations for learning and simulation algorithms. Essentially, our framework formulates stochastic transports as noisy information processes governing the dynamic translation and propagation of information between arbitrary probability measures. Our theoretical and algorithmic presentation details training and simulation frameworks for both Gaussian and L\'evy (specifically, Gamma, Poisson and Stable-$1/2$) random-bridge transports. The empirical validation focuses on the Gaussian case for demonstration and comparison purposes, where our construct delivers high-quality samples, achieving competitive Fr\'echet Inception Distance scores compared to widely used denoising diffusions and flow matching frameworks.
Abstract:This paper motivates the use of random-bridges -- stochastic processes conditioned to take target distributions at fixed timepoints -- in the realm of generative modelling. Herein, random-bridges act as stochastic transports between two probability distributions when appropriately initialized, displaying either Markovian or non-Markovian, and continuous, discontinuous, or hybrid patterns depending on the choice of the driving process. We show how one can start from general probabilistic statements and branch out into specific representations for learning and simulation algorithms. Essentially, our framework formulates stochastic transports as noisy information processes governing the dynamic translation and propagation of information between arbitrary probability measures. Our theoretical and algorithmic presentation details training and simulation frameworks for both Gaussian and Lévy (specifically, Gamma, Poisson and Stable-$1/2$) random-bridge transports. The empirical validation focuses on the Gaussian case for demonstration and comparison purposes, where our construct delivers high-quality samples, achieving competitive Fréchet Inception Distance scores compared to widely used denoising diffusions and flow matching frameworks.
Machine Learning (cs.LG); Probability (math.PR)
arXiv:2512.14190 [cs.LG]
(or arXiv:2512.14190v4 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2512.14190 Focus to learn more arXiv-issued DOI via DataCite
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