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Transporting between arbitrary distributions is a fundamental goal in generative modeling. Recently proposed diffusion bridge models provide a potential solution, but they rely on a joint distribution that is difficult to obtain in…

Machine Learning · Computer Science 2025-03-03 Jun Hyeong Kim , Seonghwan Kim , Seokhyun Moon , Hyeongwoo Kim , Jeheon Woo , Woo Youn Kim

The dynamic Schr\"odinger bridge problem provides an appealing setting for solving constrained time-series data generation tasks posed as optimal transport problems. It consists of learning non-linear diffusion processes using efficient…

Machine Learning · Computer Science 2023-11-27 Ella Tamir , Martin Trapp , Arno Solin

Schr\"odinger bridges (SBs) provide an elegant framework for modeling the temporal evolution of populations in physical, chemical, or biological systems. Such natural processes are commonly subject to changes in population size over time…

Machine Learning · Computer Science 2023-06-16 Matteo Pariset , Ya-Ping Hsieh , Charlotte Bunne , Andreas Krause , Valentin De Bortoli

The Schr\"odinger bridge problem seeks the optimal stochastic process that connects two given probability distributions with minimal energy modification. While the Sinkhorn algorithm is widely used to solve the static optimal transport…

Machine Learning · Statistics 2025-10-28 Ibuki Maeda , Rentian Yao , Atsushi Nitanda

Multi-marginal Optimal Transport (mOT), a generalization of OT, aims at minimizing the integral of a cost function with respect to a distribution with some prescribed marginals. In this paper, we consider an entropic version of mOT with a…

Machine Learning · Statistics 2023-10-31 Maxence Noble , Valentin De Bortoli , Arnaud Doucet , Alain Durmus

Score-based generative models have recently attracted significant attention for their ability to generate high-fidelity data by learning maps from simple Gaussian priors to complex data distributions. A natural generalization of this idea…

Computation · Statistics 2025-11-19 Hanwen Huang

The Schr\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certain transportation cost. This problem, which represents a generalisation of optimal transport…

Machine Learning · Computer Science 2026-03-03 Kirill Tamogashev , Nikolay Malkin

Schr\"{o}dinger bridge is a stochastic optimal control problem to steer a given initial state density to another, subject to controlled diffusion and deadline constraints. A popular method to numerically solve the Schr\"{o}dinger bridge…

Optimization and Control · Mathematics 2023-09-14 Alexis M. H. Teter , Yongxin Chen , Abhishek Halder

Schrodinger Bridges (SBs) are diffusion processes that steer, in finite time, a given initial distribution to another final one while minimizing a suitable cost functional. Although various methods for computing SBs have recently been…

Machine Learning · Computer Science 2025-10-15 George Rapakoulias , Ali Reza Pedram , Fengjiao Liu , Lingjiong Zhu , Panagiotis Tsiotras

Generating samples from a probability distribution is a fundamental task in machine learning and statistics. This article proposes a novel scheme for sampling from a distribution for which the probability density $\mu({\bf x})$ for ${\bf…

Computation · Statistics 2024-05-22 Hanwen Huang

Independent sample generation is the prevailing paradigm in modern diffusion-based generative models of AI. We ask a different question: can samples \emph{coordinate} through shared population statistics to transport probability mass more…

Optimization and Control · Mathematics 2026-05-04 Michael Chertkov

Given two boundary distributions, the Schr\"odinger Bridge (SB) problem seeks the ``most likely`` random evolution between them with respect to a reference process. It has revealed rich connections to recent machine learning methods for…

Machine Learning · Computer Science 2025-06-03 Maosheng Yang

Despite the recent advances in the field of computational Schr\"odinger Bridges (SB), most existing SB solvers are still heavy-weighted and require complex optimization of several neural networks. It turns out that there is no principal…

Machine Learning · Computer Science 2024-03-20 Alexander Korotin , Nikita Gushchin , Evgeny Burnaev

Many natural dynamic processes -- such as in vivo cellular differentiation or disease progression -- can only be observed through the lens of static sample snapshots. While challenging, reconstructing their temporal evolution to decipher…

Machine Learning · Computer Science 2025-12-08 Thomas Gravier , Thomas Boyer , Auguste Genovesio

Generative AI can be framed as the problem of learning a model that maps simple reference measures into complex data distributions, and it has recently found a strong connection to the classical theory of the Schr\"odinger bridge problems…

Machine Learning · Computer Science 2025-10-29 Jin Ma , Ying Tan , Renyuan Xu

Learning generative models in settings where the source and target distributions are only specified through unpaired samples is gaining in importance. Here, one frequently-used model are Schr\"odinger bridges (SB), which represent the most…

Machine Learning · Computer Science 2026-05-13 Tobias Fuchs , Florian Kalinke , Nadja Klein

The Entropic Optimal Transport (EOT) problem and its dynamic counterpart, the Schr\"odinger bridge (SB) problem, play an important role in modern machine learning, linking generative modeling with optimal transport theory. While recent…

In image generation, Schr\"odinger Bridge (SB)-based methods theoretically enhance the efficiency and quality compared to the diffusion models by finding the least costly path between two distributions. However, they are computationally…

Computer Vision and Pattern Recognition · Computer Science 2025-03-05 Xingyu Qiu , Mengying Yang , Xinghua Ma , Fanding Li , Dong Liang , Gongning Luo , Wei Wang , Kuanquan Wang , Shuo Li

We study the Schr\"odinger bridge problem when the endpoint distributions are available only through samples. Classical computational approaches estimate Schr\"odinger potentials via Sinkhorn iterations on empirical measures and then…

Machine Learning · Statistics 2026-02-10 Denis Belomestny , Alexey Naumov , Nikita Puchkin , Denis Suchkov

In this paper, we investigate the multi-marginal Schrodinger bridge (MSB) problem whose marginal constraints are marginal distributions of a stochastic differential equation (SDE) with a constant diffusion coefficient, and with time…

Probability · Mathematics 2025-07-15 Rentian Yao , Young--Heon Kim , Geoffrey Schiebinger