English
Related papers

Related papers: Solving Schr\"{o}dinger bridge problem via continu…

200 papers

Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…

Discrete Mathematics · Computer Science 2017-05-24 Fabian Mies , Britta Peis , Andreas Wierz

Normalizing flows are constructed from a base distribution with a known density and a diffeomorphism with a tractable Jacobian. The base density of a normalizing flow can be parameterised by a different normalizing flow, thus allowing maps…

Machine Learning · Computer Science 2022-11-07 Samuel Klein , John Andrew Raine , Tobias Golling

The numerical quantification of the statistics of rare events in stochastic processes is a challenging computational problem. We present a sampling method that constructs an ensemble of stochastic trajectories that are constrained to have…

Statistical Mechanics · Physics 2022-07-13 Javier Aguilar , Joseph W. Baron , Tobias Galla , Raul Toral

Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth…

Methodology · Statistics 2017-05-01 Gabriel Loaiza-Ganem , Yuanjun Gao , John P. Cunningham

We consider the Schr{\"o}dinger bridge problem in discrete time, where the pathwise cost is replaced by a sum of quadratic functions, taking the form of a linear quadratic regulator (LQR) cost. This cost comprises potential terms that act…

Optimization and Control · Mathematics 2025-11-25 Marc Lambert

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

We study the Schr\"odinger-Bass problem, a one-parameter family of semimartingale optimal transport problems indexed by $\beta>0$, whose limiting regimes interpolate between the classical Schr\"odinger bridge, the Brenier-Strassen problem,…

Probability · Mathematics 2026-04-03 Manuel Hasenbichler , Gudmund Pammer , Stefan Thonhauser

The Schr\"odinger Bridge (SB) problem offers a powerful framework for combining optimal transport and diffusion models. A promising recent approach to solve the SB problem is the Iterative Markovian Fitting (IMF) procedure, which alternates…

Machine Learning · Computer Science 2024-11-06 Nikita Gushchin , Daniil Selikhanovych , Sergei Kholkin , Evgeny Burnaev , Alexander Korotin

Recent advancements in diffusion bridges for distribution transport problems have heavily relied on matching frameworks, yet existing methods often face a trade-off between scalability and access to optimal pairings during training. Fully…

The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural…

Numerical Analysis · Mathematics 2024-06-04 Steffen Schotthöfer , M. Paul Laiu , Martin Frank , Cory D. Hauck

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

Deep graph neural networks (GNNs) often suffer from oversmoothing, where node representations become overly homogeneous with increasing depth. While techniques like normalization, residual connections, and edge dropout have been proposed to…

Machine Learning · Computer Science 2025-05-30 Jiaqi Wang , Xinyi Wu , James Cheng , Yifei Wang

Quantum counterparts of Schrodinger's classical bridge problem have been around for the better part of half a century. During that time, several quantum approaches to this multifaceted classical problem have been introduced. In the present…

Quantum Physics · Physics 2025-03-11 Olga Movilla Miangolarra , Ralph Sabbagh , Tryphon T. Georgiou

The Sinkhorn algorithm is the most popular method for solving the entropy minimization problem called the Schr\"odinger problem: in the non-degenerate cases, the latter admits a unique solution towards which the algorithm converges…

Optimization and Control · Mathematics 2023-02-27 Aymeric Baradat , Elias Ventre

A number of problems in relational Artificial Intelligence can be viewed as Stochastic Constraint Optimization Problems (SCOPs). These are constraint optimization problems that involve objectives or constraints with a stochastic component.…

Artificial Intelligence · Computer Science 2018-07-04 Anna L. D. Latour , Behrouz Babaki , Siegfried Nijssen

Computational methods for learning to sample from the Boltzmann distribution -- where the target distribution is known only up to an unnormalized energy function -- have advanced significantly recently. Due to the lack of explicit target…

Machine Learning · Statistics 2025-11-26 Guan-Horng Liu , Jaemoo Choi , Yongxin Chen , Benjamin Kurt Miller , Ricky T. Q. Chen

Solving inverse problems -- recovering signals from incomplete or noisy measurements -- is fundamental in science and engineering. Score-based generative models (SGMs) have recently emerged as a powerful framework for this task. Two main…

Machine Learning · Computer Science 2025-10-27 Bartlomiej Sobieski , Matthew Tivnan , Yuang Wang , Siyeop Yoon , Pengfei Jin , Dufan Wu , Quanzheng Li , Przemyslaw Biecek

Diffusion models often yield highly curved trajectories and noisy score targets due to an uninformative, memoryless forward process that induces independent data-noise coupling. We propose Adjoint Schr\"odinger Bridge Matching (ASBM), a…

Computer Vision and Pattern Recognition · Computer Science 2026-02-18 Jeongwoo Shin , Jinhwan Sul , Joonseok Lee , Jaewong Choi , Jaemoo Choi

The mean-field Schr\"odinger bridge (MFSB) problem concerns designing a minimum-effort controller that guides a diffusion process with nonlocal interaction to reach a given distribution from another by a fixed deadline. Unlike the standard…

Optimization and Control · Mathematics 2026-04-10 Asmaa Eldesoukey , Yongxin Chen , Abhishek Halder

Generative models, particularly normalizing flows, have shown exceptional performance in learning probability distributions across various domains of physics, including statistical mechanics, collider physics, and lattice field theory. In…

Strongly Correlated Electrons · Physics 2025-01-14 Dominic Schuh , Janik Kreit , Evan Berkowitz , Lena Funcke , Thomas Luu , Kim A. Nicoli , Marcel Rodekamp