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Modern distribution matching algorithms for training diffusion or flow models directly prescribe the time evolution of the marginal distributions between two boundary distributions. In this work, we consider a generalized distribution…

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 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

Predicting the intermediate trajectories between an initial and target distribution is a central problem in generative modeling. Existing approaches, such as flow matching and Schr\"odinger bridge matching, effectively learn mappings…

Machine Learning · Computer Science 2026-03-03 Sophia Tang , Yinuo Zhang , Alexander Tong , Pranam Chatterjee

Predicting single-cell perturbation outcomes directly advances gene function analysis and facilitates drug candidate selection, making it a key driver of both basic and translational biomedical research. However, a major bottleneck in this…

Machine Learning · Computer Science 2025-11-18 Changxi Chi , Yufei Huang , Jun Xia , Jiangbin Zheng , Yunfan Liu , Zelin Zang , Stan Z. Li

This paper introduces a novel theoretical simplification of the Diffusion Schr\"odinger Bridge (DSB) that facilitates its unification with Score-based Generative Models (SGMs), addressing the limitations of DSB in complex data generation…

Machine Learning · Computer Science 2024-10-30 Zhicong Tang , Tiankai Hang , Shuyang Gu , Dong Chen , Baining Guo

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 Quantum Schr\"odinger Bridge Problem (QSBP) describes the evolution of a stochastic process between two arbitrary probability distributions, where the dynamics are governed by the Schr\"odinger equation rather than by the traditional…

Machine Learning · Computer Science 2025-10-01 Mykola Bordyuh , Djork-Arné Clevert , Marco Bertolini

We consider the problem of sampling from an unknown distribution for which only a sufficiently large number of training samples are available. Such settings have recently drawn considerable interest in the context of generative modelling…

Machine Learning · Statistics 2024-10-24 Georg A. Gottwald , Fengyi Li , Youssef Marzouk , Sebastian Reich

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

Conditional generative models represent a significant advancement in the field of machine learning, allowing for the controlled synthesis of data by incorporating additional information into the generation process. In this work we introduce…

Machine Learning · Statistics 2024-09-27 Hanwen Huang

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

This work studies the Schr\"odinger bridge problem for the kinematic equation on a compact connected Lie group. The objective is to steer a controlled diffusion between given initial and terminal densities supported over the Lie group while…

Optimization and Control · Mathematics 2026-03-23 Hamza Mahmood , Abhishek Halder , Adeel Akhtar

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…

Over the last several years, there has been significant progress in developing neural solvers for the Schr\"odinger Bridge (SB) problem and applying them to generative modelling. This new research field is justifiably fruitful as it is…

The Schr\"odinger Bridge (SB) is a powerful framework for solving generative modeling tasks such as unpaired domain translation. Most SB-related research focuses on continuous data space $\mathbb{R}^{D}$ and leaves open theoretical and…

Machine Learning · Computer Science 2025-08-19 Grigoriy Ksenofontov , Alexander Korotin

Constrained machine learning enables fairness-aware training, physics-informed neural networks, and integration of symbolic domain knowledge into statistical models. Despite its practical importance, no general method exists for the…

Machine Learning · Computer Science 2026-05-20 Adam Bosák , Andrii Kliachkin , Jana Lepšová , Gilles Bareilles , Jakub Mareček

We propose a novel generative model for time series based on Schr{\"o}dinger bridge (SB) approach. This consists in the entropic interpolation via optimal transport between a reference probability measure on path space and a target measure…

Optimization and Control · Mathematics 2023-04-12 Mohamed Hamdouche , Pierre Henry-Labordere , Huyên Pham

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

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