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We introduce a novel discretization scheme for Wasserstein gradient flows that involves successively computing Schr\"{o}dinger bridges with the same marginals. This is different from both the forward/geodesic approximation and the…

Probability · Mathematics 2024-06-18 Medha Agarwal , Zaid Harchaoui , Garrett Mulcahy , Soumik Pal

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

As data sets grow in size, the ability of learning methods to find structure in them is increasingly hampered by the time needed to search the large spaces of possibilities and generate a score for each that takes all of the observed data…

Machine Learning · Computer Science 2012-07-03 Benjamin Yackley , Terran Lane

We present simulation-free score and flow matching ([SF]$^2$M), a simulation-free objective for inferring stochastic dynamics given unpaired samples drawn from arbitrary source and target distributions. Our method generalizes both the…

User cold-start problem is a long-standing challenge in recommendation systems. Fortunately, cross-domain recommendation (CDR) has emerged as a highly effective remedy for the user cold-start challenge, with recently developed diffusion…

Information Retrieval · Computer Science 2026-03-04 Xiaodong Li , Juwei Yue , Xinghua Zhang , Jiawei Sheng , Wenyuan Zhang , Taoyu Su , Zefeng Zhang , Tingwen Liu

We consider stochastic differential equations of the form $dY_t=V(Y_t)\,dX_t+V_0(Y_t)\,dt$ driven by a multi-dimensional Gaussian process. Under the assumption that the vector fields $V_0$ and $V=(V_1,\ldots,V_d)$ satisfy H\"{o}rmander's…

Probability · Mathematics 2015-01-21 Thomas Cass , Martin Hairer , Christian Litterer , Samy Tindel

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

In this work, we study a discrete Schr\"odinger bridge problem with partial marginal observations. A main difficulty compared to the classical Schr\"odinger bridge formulation is that our problem is not strictly convex and standard…

Optimization and Control · Mathematics 2026-04-08 Michele Mascherpa , Victor Molnö , Carsten Skovmose Kallesøe , Johan Karlsson

We introduce Triangular-Reference Schr\"odinger Bridges for Time Series (TR-SBTS), a conservative extension of the SBTS framework in which the Brownian reference is replaced by an intervalwise frozen, possibly degenerate diffusion…

Machine Learning · Statistics 2026-05-29 Gabriele Bocchi

Schr\"odinger bridges have emerged as an enabling framework for unveiling the stochastic dynamics of systems based on marginal observations at different points in time. The terminology "bridge'' refers to a probability law that suitably…

Statistical Mechanics · Physics 2024-03-05 Olga Movilla Miangolarra , Asmaa Eldesoukey , Tryphon T. Georgiou

Understanding traffic participants' behaviour is crucial for predicting their future trajectories, aiding in developing safe and reliable planning systems for autonomous vehicles. Integrating cognitive processes and machine learning models…

Machine Learning · Computer Science 2023-06-05 Frederik S. B. Westerhout , Julian F. Schumann , Arkady Zgonnikov

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

Generative AI can be framed as the problem of learning a model that maps simple reference measures into complex data distributions, and it has recently found a strong connection to the classical theory of the Schr\"odinger bridge problems…

Machine Learning · Computer Science 2025-10-29 Jin Ma , Ying Tan , Renyuan Xu

Flow matching and diffusion bridge models have emerged as leading paradigms in generative speech enhancement, modeling stochastic processes between paired noisy and clean speech signals based on principles such as flow matching, score…

Audio and Speech Processing · Electrical Eng. & Systems 2026-02-23 Dahan Wang , Jun Gao , Tong Lei , Yuxiang Hu , Changbao Zhu , Kai Chen , Jing Lu

The Schr\"{o}dinger Bridge Problem (SBP), which can be understood as an entropy-regularized optimal transport, seeks to compute stochastic dynamic mappings connecting two given distributions. SBP has shown significant theoretical importance…

Optimization and Control · Mathematics 2025-03-25 Yang Jing , Lei Li , Jingtong Zhang

Many statistical problems include model parameters that are defined as the solutions to optimization sub-problems. These include classical approaches such as profile likelihood as well as modern applications involving flow networks or…

Methodology · Statistics 2025-03-17 Cheng Zeng , Yaozhi Yang , Jason Xu , Leo L Duan

Schr\"odinger bridge (SB) has emerged as the go-to method for optimizing transportation plans in diffusion models. However, SB requires estimating the intractable forward score functions, inevitably resulting in the costly implicit training…

Machine Learning · Computer Science 2025-05-27 Wei Deng , Weijian Luo , Yixin Tan , Marin Biloš , Yu Chen , Yuriy Nevmyvaka , Ricky T. Q. Chen

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

In the early 1930's, Erwin Schroedinger, motivated by his quest for a more classical formulation of quantum mechanics, posed a large deviation problem for a cloud of independent Brownian particles. He showed that the solution to the problem…

Optimization and Control · Mathematics 2018-09-21 Montacer Essid , 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