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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,…

The Schrodinger Bridge and Bass (SBB) formulation, which jointly controls drift and volatility, is an established extension of the classical Schrodinger Bridge (SB). Building on this framework, we introduce LightSBB-M, an algorithm that…

Machine Learning · Computer Science 2026-05-06 Alexandre Alouadi , Pierre Henry-Labordère , Grégoire Loeper , Othmane Mazhar , Huyên Pham , Nizar Touzi

Accurate and reliable prediction has profound implications to a wide range of applications. In this study, we focus on an instance of spatio-temporal learning problem--traffic prediction--to demonstrate an advanced deep learning model…

Machine Learning · Computer Science 2024-08-27 Pingping Dong , Xiao-Lin Wang , Indranil Bose , Kam K. H. Ng , Xiaoning Zhang , Xiaoge Zhang

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

Diffusion Schr\"odinger bridges (DSB) have recently emerged as a powerful framework for recovering stochastic dynamics via their marginal observations at different time points. Despite numerous successful applications, existing algorithms…

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

The Schr\"odinger Bridge (SB) problem has become a fundamental tool in computational optimal transport and generative modeling. To address this problem, ideal methods such as Iterative Proportional Fitting and Iterative Markovian Fitting…

Machine Learning · Statistics 2025-10-27 Marta Gentiloni Silveri , Giovanni Conforti , Alain Durmus

The Schr\"odinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have…

Machine Learning · Statistics 2022-05-31 Francisco Vargas , Pierre Thodoroff , Neil D. Lawrence , Austen Lamacraft

Causal discovery in the presence of missing data introduces a chicken-and-egg dilemma. While the goal is to recover the true causal structure, robust imputation requires considering the dependencies or, preferably, causal relations among…

Machine Learning · Computer Science 2024-06-04 Vy Vo , He Zhao , Trung Le , Edwin V. Bonilla , Dinh Phung

In this paper, we introduce a framework for contextual distributionally robust optimization (DRO) that considers the causal and continuous structure of the underlying distribution by developing interpretable and tractable decision rules…

Machine Learning · Statistics 2026-04-03 Fenglin Zhang , Jie Wang

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…

We investigate the generative capabilities of the Schr\"odinger Bridge (SB) approach for time series. The SB framework formulates time series synthesis as an entropic optimal interpolation transport problem between a reference probability…

Machine Learning · Computer Science 2025-10-27 Alexandre Alouadi , Baptiste Barreau , Laurent Carlier , Huyên Pham

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

The momentum Schr\"odinger Bridge (mSB) has emerged as a leading method for accelerating generative diffusion processes and reducing transport costs. However, the lack of simulation-free properties inevitably results in high training costs…

Machine Learning · Statistics 2025-01-29 Kevin Rojas , Yixin Tan , Molei Tao , Yuriy Nevmyvaka , Wei Deng

Motivated by modern machine learning applications where we only have access to empirical measures constructed from finite samples, we relax the marginal constraints of the classical Schr\"odinger bridge problem by penalizing the transport…

Probability · Mathematics 2026-02-10 Yifan Jiang , Renyuan Xu , Luhao Zhang

Optimal transport (OT) and Schr{\"o}dinger bridge (SB) problems have emerged as powerful frameworks for transferring probability distributions with minimal cost. However, existing approaches typically focus on endpoint matching while…

Optimization and Control · Mathematics 2025-10-09 Xu Duan , Dongmei Chen

Solving transport problems, i.e. finding a map transporting one given distribution to another, has numerous applications in machine learning. Novel mass transport methods motivated by generative modeling have recently been proposed, e.g.…

Machine Learning · Statistics 2023-12-13 Yuyang Shi , Valentin De Bortoli , Andrew Campbell , Arnaud Doucet

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

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