English
Related papers

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

200 papers

In image generation, Schr\"odinger Bridge (SB)-based methods theoretically enhance the efficiency and quality compared to the diffusion models by finding the least costly path between two distributions. However, they are computationally…

Computer Vision and Pattern Recognition · Computer Science 2025-03-05 Xingyu Qiu , Mengying Yang , Xinghua Ma , Fanding Li , Dong Liang , Gongning Luo , Wei Wang , Kuanquan Wang , Shuo Li

Leveraging connections between diffusion-based sampling, optimal transport, and stochastic optimal control through their shared links to the Schr\"odinger bridge problem, we propose novel objective functions that can be used to transport…

Machine Learning · Statistics 2024-10-11 Qijia Jiang , David Nabergoj

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

Monge-Kantorovich optimal mass transport (OMT) provides a blueprint for geometries in the space of positive densities -- it quantifies the cost of transporting a mass distribution into another. In particular, it provides natural options for…

Optimization and Control · Mathematics 2015-06-16 Yongxin Chen , Tryphon T. Georgiou , Michele Pavon

Consider the problem of matching two independent i.i.d. samples of size $N$ from two distributions $P$ and $Q$ in $\mathbb{R}^d$. For an arbitrary continuous cost function, the optimal assignment problem looks for the matching that…

Probability · Mathematics 2023-01-03 Zaid Harchaoui , Lang Liu , Soumik Pal

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

The bridge problem is to find an SDE (or sometimes an ODE) that bridges two given distributions. The application areas of the bridge problem are enormous, among which the recent generative modeling (e.g., conditional or unconditional image…

Machine Learning · Computer Science 2025-09-15 Minyoung 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

Quantum counterparts of Schrodinger's classical bridge problem have been around for the better part of half a century. During that time, several quantum approaches to this multifaceted classical problem have been introduced. In the present…

Quantum Physics · Physics 2025-03-11 Olga Movilla Miangolarra , Ralph Sabbagh , Tryphon T. Georgiou

Score-based generative models have recently attracted significant attention for their ability to generate high-fidelity data by learning maps from simple Gaussian priors to complex data distributions. A natural generalization of this idea…

Computation · Statistics 2025-11-19 Hanwen Huang

We consider the problem to steer a linear dynamical system with full state observation from an initial gaussian distribution in state-space to a final one with minimum energy control. The system is stochastically driven through the control…

Systems and Control · Computer Science 2014-08-12 Yongxin Chen , Tryphon Georgiou , Michele Pavon

Density ratio estimation is fundamental to tasks involving $f$-divergences, yet existing methods often fail under significantly different distributions or inadequately overlapping supports -- the density-chasm and the support-chasm…

Machine Learning · Computer Science 2025-11-04 Wei Chen , Shigui Li , Jiacheng Li , Junmei Yang , John Paisley , Delu Zeng

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

Deep Ensemble (DE) approach is a straightforward technique used to enhance the performance of deep neural networks by training them from different initial points, converging towards various local optima. However, a limitation of this…

Machine Learning · Computer Science 2024-04-25 Hyunsu Kim , Jongmin Yoon , Juho Lee

Diffusion models (DMs), which enable both image generation from noise and inversion from data, have inspired powerful unpaired image-to-image (I2I) translation algorithms. However, they often require a larger number of neural function…

Computer Vision and Pattern Recognition · Computer Science 2024-11-25 Jeongsol Kim , Beomsu Kim , Jong Chul Ye

Image inpainting is an important image generation task, which aims to restore corrupted image from partial visible area. Recently, diffusion Schr\"odinger bridge methods effectively tackle this task by modeling the translation between…

Computer Vision and Pattern Recognition · Computer Science 2024-12-12 Zihao Han , Baoquan Zhang , Lisai Zhang , Shanshan Feng , Kenghong Lin , Guotao Liang , Yunming Ye , Xiaochen Qi , Guangming Ye

The static optimal transport $(\mathrm{OT})$ problem between Gaussians seeks to recover an optimal map, or more generally a coupling, to morph a Gaussian into another. It has been well studied and applied to a wide variety of tasks. Here we…

Machine Learning · Computer Science 2023-04-03 Charlotte Bunne , Ya-Ping Hsieh , Marco Cuturi , Andreas Krause

We propose Image-to-Image Schr\"odinger Bridge (I$^2$SB), a new class of conditional diffusion models that directly learn the nonlinear diffusion processes between two given distributions. These diffusion bridges are particularly useful for…

Computer Vision and Pattern Recognition · Computer Science 2023-05-29 Guan-Horng Liu , Arash Vahdat , De-An Huang , Evangelos A. Theodorou , Weili Nie , Anima Anandkumar

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