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Related papers: Schr\"odinger Bridge Problem for Jump Diffusions

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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

At the core of modern generative modeling frameworks, including diffusion models, score-based models, and flow matching, is the task of transforming a simple prior distribution into a complex target distribution through stochastic paths in…

Machine Learning · Computer Science 2026-03-20 Sophia Tang

We study the Schr\"{o}dinger bridge problem (SBP) with nonlinear prior dynamics. In control-theoretic language, this is a problem of minimum effort steering of a given joint state probability density function (PDF) to another over a finite…

Optimization and Control · Mathematics 2021-03-17 Kenneth F. Caluya , Abhishek Halder

Consider a reference Markov process with initial distribution $\pi_{0}$ and transition kernels $\{M_{t}\}_{t\in[1:T]}$, for some $T\in\mathbb{N}$. Assume that you are given distribution $\pi_{T}$, which is not equal to the marginal…

Computation · Statistics 2020-01-01 Espen Bernton , Jeremy Heng , Arnaud Doucet , Pierre E. Jacob

The dynamic Schr\"odinger bridge problem seeks a stochastic process that defines a transport between two target probability measures, while optimally satisfying the criteria of being closest, in terms of Kullback-Leibler divergence, to a…

Machine Learning · Statistics 2023-12-25 Stefano Peluchetti

Recent diffusion probabilistic models (DPM) in the field of pansharpening have been gradually gaining attention and have achieved state-of-the-art (SOTA) performance. In this paper, we identify shortcomings in directly applying DPMs to the…

Computer Vision and Pattern Recognition · Computer Science 2024-04-18 Zihan Cao , Xiao Wu , Liang-Jian Deng

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

We consider the problem of simulating diffusion bridges, which are diffusion processes that are conditioned to initialize and terminate at two given states. The simulation of diffusion bridges has applications in diverse scientific fields…

Computation · Statistics 2025-06-19 Jeremy Heng , Valentin De Bortoli , Arnaud Doucet , James Thornton

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

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

We study a semimartingale optimal transport problem interpolating between the Schr\"odinger bridge and the stretched Brownian motion associated with the Bass solution of the Skorokhod embedding problem. The cost combines an entropy term on…

Probability · Mathematics 2026-03-31 Pierre Henry-Labordere , Grégoire Loeper , Othmane Mazhar , Huyên Pham , Nizar Touzi

The subject of this work has its roots in the so called Schroedginer Bridge Problem (SBP) which asks for the most likely distribution of Brownian particles in their passage between observed empirical marginal distributions at two distinct…

Systems and Control · Computer Science 2016-08-15 Yongxin Chen , Tryphon T. Georgiou , Michele Pavon

Schr\"{o}dinger bridge is a diffusion process that steers a given distribution to another in a prescribed time while minimizing the effort to do so. It can be seen as the stochastic dynamical version of the optimal mass transport, and has…

Optimization and Control · Mathematics 2024-10-29 Alexis M. H. Teter , Wenqing Wang , Abhishek Halder

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…

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

In 1931/32, Schroedinger studied a hot gas Gedankenexperiment, an instance of large deviations of the empirical distribution and an early example of the so-called maximum entropy inference method. This so-called Schroedinger bridge problem…

Optimization and Control · Mathematics 2020-11-30 Yongxin Chen , Tryphon T. Georgiou , Michele Pavon

The Schr\"odinger bridge problem seeks the optimal stochastic process that connects two given probability distributions with minimal energy modification. While the Sinkhorn algorithm is widely used to solve the static optimal transport…

Machine Learning · Statistics 2025-10-28 Ibuki Maeda , Rentian Yao , Atsushi Nitanda

Schrodinger Bridges (SBs) are diffusion processes that steer, in finite time, a given initial distribution to another final one while minimizing a suitable cost functional. Although various methods for computing SBs have recently been…

Machine Learning · Computer Science 2025-10-15 George Rapakoulias , Ali Reza Pedram , Fengjiao Liu , Lingjiong Zhu , Panagiotis Tsiotras

In this paper, we investigate the multi-marginal Schrodinger bridge (MSB) problem whose marginal constraints are marginal distributions of a stochastic differential equation (SDE) with a constant diffusion coefficient, and with time…

Probability · Mathematics 2025-07-15 Rentian Yao , Young--Heon Kim , Geoffrey Schiebinger

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