Related papers: Multi-marginal temporal Schr\"odinger Bridge Match…

Recent advancements in diffusion bridges for distribution transport problems have heavily relied on matching frameworks, yet existing methods often face a trade-off between scalability and access to optimal pairings during training. Fully…

Audio-visual deepfake localization demands interval-level outputs that serve as temporal evidence. Despite recent progress, symmetric fusion under single-sided or asynchronous forgeries propagates cross-modal noise, degrading high-precision…

Multi-modal brain MRI provides essential complementary information for clinical diagnosis. However, acquiring all modalities in practice is often constrained by time and cost. To address this, various methods have been proposed to generate…

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…

Generative modeling typically seeks the path of least action via deterministic flows (ODE). While effective for in-distribution tasks, we argue that these deterministic paths become brittle under causal interventions, which often require…

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…

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…

Progressively applying Gaussian noise transforms complex data distributions to approximately Gaussian. Reversing this dynamic defines a generative model. When the forward noising process is given by a Stochastic Differential Equation (SDE),…

Mass transport problems arise in many areas of machine learning whereby one wants to compute a map transporting one distribution to another. Generative modeling techniques like Generative Adversarial Networks (GANs) and Denoising Diffusion…

The solution of the path structured multimarginal Schr\"{o}dinger bridge problem (MSBP) is the most-likely measure-valued trajectory consistent with a sequence of observed probability measures or distributional snapshots. We leverage recent…

We study the problem of identifying an optimal coupling between input-output distributional data generated by a causal dynamical system. The coupling is required to satisfy prescribed marginal distributions and a causality constraint…

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…

Score-based diffusion models are frequently employed as structural priors in inverse problems. However, their iterative denoising process, initiated from Gaussian noise, often results in slow inference speeds. The Image-to-Image…

Multi-marginal Optimal Transport (mOT), a generalization of OT, aims at minimizing the integral of a cost function with respect to a distribution with some prescribed marginals. In this paper, we consider an entropic version of mOT with a…

Resampling from a target measure whose density is unknown is a fundamental problem in mathematical statistics and machine learning. A setting that dominates the machine learning literature consists of learning a map from an easy-to-sample…

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…

The Schr\"odinger bridge problem (SBP) is gaining increasing attention in generative modeling and showing promising potential even in comparison with the score-based generative models (SGMs). SBP can be interpreted as an entropy-regularized…

The analysis of dynamical systems is a fundamental tool in the natural sciences and engineering. It is used to understand the evolution of systems as large as entire galaxies and as small as individual molecules. With predefined conditions…

The optimal transport problem has recently developed into a powerful framework for various applications in estimation and control. Many of the recent advances in the theory and application of optimal transport are based on regularizing the…

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…