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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

Modern methods of generative modelling and unpaired data translation based on Schr\"odinger bridges and stochastic optimal control theory aim to transform an initial density to a target one in an optimal way. In the present paper, we assume…

Machine Learning · Computer Science 2026-03-24 Nikita Puchkin , Denis Suchkov , Alexey Naumov , Denis Belomestny

Recent diffusion probabilistic models (DPM) in the field of pansharpening have been gradually gaining attention and have achieved state-of-the-art (SOTA) performance. In this paper, we identify shortcomings in directly applying DPMs to the…

Computer Vision and Pattern Recognition · Computer Science 2024-04-18 Zihan Cao , Xiao Wu , Liang-Jian Deng

The purpose of the present work is to expand substantially the type of control and estimation problems that can be addressed following the paradigm of Schr\"odinger bridges, by incorporating termination (killing) of stochastic flows.…

Optimization and Control · Mathematics 2024-06-24 Asmaa Eldesoukey , Olga Movilla Miangolarra , Tryphon T. Georgiou

The problem of reconciling a prior probability law on paths with data was introduced by E. Schr\"odinger in 1931/32. It represents an early formulation of a maximum likelihood problem. This specific formulation can also be seen as the…

Systems and Control · Electrical Eng. & Systems 2024-12-13 Asmaa Eldesoukey , Tryphon T. Georgiou

We consider the problem to steer a linear dynamical system with full state observation from an initial gaussian distribution in state-space to a final one with minimum energy control. The system is stochastically driven through the control…

Systems and Control · Computer Science 2014-08-12 Yongxin Chen , Tryphon Georgiou , Michele Pavon

The Schr\"{o}dinger bridge (SB) has evolved into a universal class of probabilistic generative models. In practice, however, estimated learning signals are innately uncertain, and the reliability promised by existing methods is often based…

Machine Learning · Computer Science 2025-12-23 Dong-Sig Han , Jaein Kim , Hee Bin Yoo , Byoung-Tak Zhang

In this work we explore a new framework for approximate Bayesian inference in large datasets based on stochastic control (i.e. Schr\"odinger bridges). We advocate stochastic control as a finite time and low variance alternative to popular…

The static optimal transport $(\mathrm{OT})$ problem between Gaussians seeks to recover an optimal map, or more generally a coupling, to morph a Gaussian into another. It has been well studied and applied to a wide variety of tasks. Here we…

Machine Learning · Computer Science 2023-04-03 Charlotte Bunne , Ya-Ping Hsieh , Marco Cuturi , Andreas Krause

We take a new look at the relation between the optimal transport problem and the Schr\"{o}dinger bridge problem from the stochastic control perspective. We show that the connections are richer and deeper than described in existing…

Systems and Control · Computer Science 2014-12-16 Yongxin Chen , Tryphon Georgiou , Michele Pavon

We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…

Machine Learning · Computer Science 2023-11-02 Nikita Gushchin , Alexander Kolesov , Alexander Korotin , Dmitry Vetrov , Evgeny Burnaev

Consider the problem of matching two independent i.i.d. samples of size $N$ from two distributions $P$ and $Q$ in $\mathbb{R}^d$. For an arbitrary continuous cost function, the optimal assignment problem looks for the matching that…

Probability · Mathematics 2023-01-03 Zaid Harchaoui , Lang Liu , Soumik Pal

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

This short paper announces the main results of \cite{SBB2026}, where the Schr\"odinger--Bass Bridge (SBB) problem is introduced and studied in full generality. Here we provide a direct PDE derivation of the SBB system in dimension one,…

We study the least-energy way to reshape a probability distribution when motion is constrained to a horizontal bundle, that is, optimal transport and distribution steering in sub-Riemannian geometry, motivated by density control over…

Optimization and Control · Mathematics 2026-05-18 Daniel Owusu Adu , Karthik Elamvazhuthi , Bahman Gharesifard

Probablistic solutions of the so called Schr\"{o}dinger boundary data problem provide for a unique Markovian interpolation between any two strictly positive probability densities designed to form the input-output statistics data for a…

Quantum Physics · Physics 2007-05-23 P. Garbaczewski

A computational PDE-constrained optimization approach is proposed for optimal trajectory planning under uncertainty by means of an associated Schroedinger Bridge Problem (SBP). The proposed SBP formulation is interpreted as the mean-field…

Optimization and Control · Mathematics 2026-05-20 Dante Kalise , Wenxin Liu

We consider a Schr\"odinger bridge problem where the Markov process is subject to parameter perturbations, forming an ensemble of systems. Our objective is to steer this ensemble from the initial distribution to the final distribution using…

Optimization and Control · Mathematics 2024-12-05 Daniel Owusu Adu , Yongxin Chen

Homotopy approaches to Bayesian inference have found widespread use especially if the Kullback-Leibler divergence between the prior and the posterior distribution is large. Here we extend one of these homotopy approach to include an…

Numerical Analysis · Mathematics 2022-11-04 Sebastian Reich

This paper exploit the equivalence between the Schr\"odinger Bridge problem and the entropy penalized optimal transport in order to find a different approach to the duality, in the spirit of optimal transport. This approach results in a…

Probability · Mathematics 2019-11-19 Simone Di Marino , Augusto Gerolin