Related papers: BM$^2$: Coupled Schr\"{o}dinger Bridge Matching

We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…

Metric learning is a fundamental problem in computer vision whereby a model is trained to learn a semantically useful embedding space via ranking losses. Traditionally, the effectiveness of a ranking loss depends on the minibatch size, and…

This technical note studies the distributed average tracking problem for multiple time-varying signals with general linear dynamics, whose reference inputs are nonzero and not available to any agent in the network. In distributed fashion, a…

Diffusion Bridge and Flow Matching have both demonstrated compelling empirical performance in transformation between arbitrary distributions. However, there remains confusion about which approach is generally preferable, and the substantial…

Transfer learning enhances the training of novel sensory and decision models by employing rich feature representations from large, pre-trained teacher models. Cognitive neuroscience shows that the human brain creates low-dimensional,…

Accurate modeling of system dynamics holds intriguing potential in broad scientific fields including cytodynamics and fluid mechanics. This task often presents significant challenges when (i) observations are limited to cross-sectional…

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…

Cross-lingual cross-modal retrieval has garnered increasing attention recently, which aims to achieve the alignment between vision and target language (V-T) without using any annotated V-T data pairs. Current methods employ machine…

Diffusion bridge models have recently become a powerful tool in the field of generative modeling. In this work, we leverage their power to address another important problem in machine learning and information theory, the estimation of the…

The \emph{Schr\"odinger problem} is obtained by replacing the mean square distance with the relative entropy in the Monge-Kantorovich problem. It was first addressed by Schr\"odinger as the problem of describing the most likely evolution of…

Diffusion models (DMs) have become the dominant paradigm of generative modeling in a variety of domains by learning stochastic processes from noise to data. Recently, diffusion denoising bridge models (DDBMs), a new formulation of…

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…

A paradigm put forth by E. Schr\"odinger in 1931/32, known as Schr\"odinger bridges, represents a formalism to pose and solve control and estimation problems seeking a perturbation from an initial control schedule (in the case of control),…

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…

The reconstruction of physical fields from sparse measurements is pivotal in both scientific research and engineering applications. Traditional methods are increasingly supplemented by deep learning models due to their efficacy in…

The numerical quantification of the statistics of rare events in stochastic processes is a challenging computational problem. We present a sampling method that constructs an ensemble of stochastic trajectories that are constrained to have…

We define a message-passing algorithm for computing magnetizations in Restricted Boltzmann machines, which are Ising models on bipartite graphs introduced as neural network models for probability distributions over spin configurations. To…

Modeling the dynamics from sparsely time-resolved snapshot data is crucial for understanding complex cellular processes and behavior. Existing methods leverage optimal transport, Schr\"odinger bridge theory, or their variants to…

We introduce Bridged Clustering, a semi-supervised framework to learn predictors from any unpaired input $X$ and output $Y$ dataset. Our method first clusters $X$ and $Y$ independently, then learns a sparse, interpretable bridge between…

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…