English
Related papers

Related papers: Control and estimation of multi-commodity network …

200 papers

Since the early nineties, it has been observed that the Schroedinger bridge problem can be formulated as a stochastic control problem with atypical boundary constraints. This in turn has a fluid dynamic counterpart where the flow of…

Probability · Mathematics 2016-01-20 Yongxin Chen , Tryphon Georgiou , Michele Pavon

For a fixed flow-based generative model under a small inference budget, sample quality can depend strongly on where the sampler spends its few function evaluations. Flow matching and Schr\"odinger bridges define probability paths, yet their…

Machine Learning · Computer Science 2026-05-18 Bruno Trentini , Dejan Stancevic , Michael M. Bronstein , Alexander Tong , Luca Ambrogioni

The Schr\"odinger bridge problem (SBP) is gaining increasing attention in generative modeling and showing promising potential even in comparison with the score-based generative models (SGMs). SBP can be interpreted as an entropy-regularized…

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

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

A Schr\"odinger bridge is the most probable time-dependent probability distribution that connects an initial probability distribution $w_{i}$ to a final one $w_{f}$. The problem has been solved and widely used for the case of simple…

Statistical Mechanics · Physics 2025-07-02 Henri Orland

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

We study single commodity network flows with suitable robustness and efficiency specs. An original use of a maximum entropy problem for distributions on the paths of the graph turns this problem into a steering problem for Markov chains…

Mathematical Physics · Physics 2017-09-28 Yongxin Chen , Tryphon T. Georgiou , Michele Pavon , Allen Tannenbaum

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

Stochastic flows of an advective-diffusive nature are ubiquitous in physical sciences. Of particular interest is the problem to reconcile observed marginal distributions with a given prior posed by E. Schrodinger in 1932/32 and known as the…

Mathematical Physics · Physics 2021-08-09 Yongxin Chen , Tryphon T. Georgiou , Michele Pavon

The \emph{Schr\"odinger problem} is obtained by replacing the mean square distance with the relative entropy in the Monge-Kantorovich problem. It was first addressed by Schr\"odinger as the problem of describing the most likely evolution of…

Probability · Mathematics 2018-06-22 Giovanni Conforti

Erwin Schroedinger posed, and to a large extent solved in 1931/32 the problem of finding the most likely random evolution between two continuous probability distributions. This article considers this problem in the case when only samples of…

Optimization and Control · Mathematics 2018-06-07 Michele Pavon , Esteban G Tabak , Giulio Trigila

The dynamic Schr\"odinger bridge problem seeks a stochastic process that defines a transport between two target probability measures, while optimally satisfying the criteria of being closest, in terms of Kullback-Leibler divergence, to a…

Machine Learning · Statistics 2023-12-25 Stefano Peluchetti

This paper introduces a dynamic formulation of divergence-regularized optimal transport with weak targets on the path space. In our formulation, the classical relative entropy penalty is replaced by a general convex divergence, and terminal…

Probability · Mathematics 2026-03-31 Camilo Hernández , Ludovic Tangpi

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

The solution of the path structured multimarginal Schr\"{o}dinger bridge problem (MSBP) is the most-likely measure-valued trajectory consistent with a sequence of observed probability measures or distributional snapshots. We leverage recent…

Systems and Control · Electrical Eng. & Systems 2023-10-05 Georgiy A. Bondar , Robert Gifford , Linh Thi Xuan Phan , Abhishek Halder

Recent advances in flow-based generative modelling have provided scalable methods for computing the Schr\"odinger Bridge (SB) between distributions, a dynamic form of entropy-regularised Optimal Transport (OT) for the quadratic cost. The…

Machine Learning · Statistics 2025-11-04 Samuel Howard , Peter Potaptchik , George Deligiannidis

Schr\"{o}dinger bridge can be viewed as a continuous-time stochastic control problem where the goal is to find an optimally controlled diffusion process whose terminal distribution coincides with a pre-specified target distribution. We…

Machine Learning · Statistics 2024-04-23 Jhanvi Garg , Xianyang Zhang , Quan Zhou

Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique dates back to the early work of Schr\"odinger. This approach…

Analysis of PDEs · Mathematics 2017-01-10 Guillaume Carlier , Vincent Duval , Gabriel Peyré , Bernhard Schmitzer

We investigate the kinetic Schr\"odinger problem, obtained considering Langevin dynamics instead of Brownian motion in Schr\"odinger's thought experiment. Under a quasilinearity assumption we establish exponential entropic turnpike…

Probability · Mathematics 2022-09-09 Alberto Chiarini , Giovanni Conforti , Giacomo Greco , Zhenjie Ren