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Related papers: Trajectory Inference with Smooth Schr\"odinger Bri…

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We study generative modeling for time series using entropic optimal transport and the Schr\"odinger bridge (SB) framework, with a focus on applications in finance and energy modeling. Extending the diffusion-based approach of Hamdouche,…

Mathematical Finance · Quantitative Finance 2026-02-24 Stefano De Marco , Huyên Pham , Davide Zanni

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

Homotopy approaches to Bayesian inference have found widespread use especially if the Kullback-Leibler divergence between the prior and the posterior distribution is large. Here we extend one of these homotopy approach to include an…

Numerical Analysis · Mathematics 2022-11-04 Sebastian Reich

How to steer a given joint state probability density function to another over finite horizon subject to a controlled stochastic dynamics with hard state (sample path) constraints? In applications, state constraints may encode safety…

Optimization and Control · Mathematics 2020-04-07 Kenneth F. Caluya , Abhishek Halder

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

We present a collection of explicit diffusion approximations to small temperature Schr\"{o}dinger bridges on manifolds. Our most precise results are when both marginals are the same and the Schr\"{o}dinger bridge is on a manifold with a…

Probability · Mathematics 2025-12-23 Garrett Mulcahy , Soumik Pal

This work introduces a novel nonlinear optimal filtering method, termed the Ensemble Schr{\"o}dinger Bridge nonlinear filter. The proposed filter combines the standard prediction step with a diffusion-generative-modeling-based analysis…

Machine Learning · Computer Science 2026-05-12 Hui Sun

Transporting between arbitrary distributions is a fundamental goal in generative modeling. Recently proposed diffusion bridge models provide a potential solution, but they rely on a joint distribution that is difficult to obtain in…

Machine Learning · Computer Science 2025-03-03 Jun Hyeong Kim , Seonghwan Kim , Seokhyun Moon , Hyeongwoo Kim , Jeheon Woo , Woo Youn Kim

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 classical Schrodinger bridge seeks the most likely probability law for a diffusion process, in path space, that matches marginals at two end points in time; the likelihood is quantified by the relative entropy between the sought law and…

Mathematical Physics · Physics 2015-06-19 Tryphon T. Georgiou , Michele Pavon

By recursively solving the underlying Schr\" odinger equation, we set up an efficient systematic approach for deriving analytic expressions for discretized effective actions. With this we obtain discrete short-time propagators for both one…

Statistical Mechanics · Physics 2011-08-08 Antun Balaz , Aleksandar Bogojevic , Ivana Vidanovic , Axel Pelster

Sequential recommendation has attracted increasing attention due to its ability to accurately capture the dynamic changes in user interests. We have noticed that generative models, especially diffusion models, which have achieved…

Information Retrieval · Computer Science 2024-09-18 Wenjia Xie , Rui Zhou , Hao Wang , Tingjia Shen , Enhong Chen

We investigate the martingale Schr\"odinger bridge, recently introduced by Nutz and Wiesel as a distinguished martingale transport plan between two probability measures in convex order. We show that this construction extends naturally to…

Probability · Mathematics 2026-05-14 Julio Backhoff , Mathias Beiglböck , Giorgia Bifronte , Armand Ley

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

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

Generative diffusion models use time-forward and backward stochastic differential equations to connect the data and prior distributions. While conventional diffusion models (e.g., score-based models) only learn the backward process, more…

Machine Learning · Computer Science 2024-12-25 Kentaro Kaba , Reo Shimizu , Masayuki Ohzeki , Yuki Sughiyama

In this paper, we study the Schr\"odinger Bridge Problem (SBP), which is central to entropic optimal transport. For general reference processes and begin--endpoint distributions, we propose a forward-reverse iterative Monte Carlo procedure…

Machine Learning · Statistics 2025-07-02 Denis Belomestny , John. Schoenmakers

We study the problem of generating synthetic time series that reproduce both marginal distributions and temporal dynamics, a central challenge in financial machine learning. Existing approaches typically fail to jointly model drift and…

Machine Learning · Computer Science 2026-04-10 Alexandre Alouadi , Grégoire Loeper , Célian Marsala , Othmane Mazhar , Huyên Pham

We study nonparametric estimation of Schr\"odinger bridge (SB) drifts from i.i.d.\ data observed on a single time interval. Starting from the conditional-ratio form of the Schr\"odinger bridge time-series (SBTS) drift formula, we analyze a…

Statistics Theory · Mathematics 2026-05-08 Othmane Mazhar , Huyên Pham

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