Related papers: The Schr\"odinger Bridge between Gaussian Measures…
Optimal transport (OT) is a powerful geometric tool used to compare and align probability measures following the least effort principle. Despite its widespread use in machine learning (ML), OT problem still bears its computational burden,…
The relevance of optimal transport methods to machine learning has long been hindered by two salient limitations. First, the $O(n^3)$ computational cost of standard sample-based solvers (when used on batches of $n$ samples) is prohibitive.…
It is a crucial challenge to reconstruct population dynamics using unlabeled samples from distributions at coarse time intervals. Recent approaches such as flow-based models or Schr\"odinger Bridge (SB) models have demonstrated appealing…
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…
The Schr\"odinger Bridge provides a principled framework for modeling stochastic processes between distributions; however, existing methods are limited by energy-conservation assumptions, which constrains the bridge's shape preventing it…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
Optimal transport (OT) theory provides a principled framework for modeling mass movement in applications such as mobility, logistics, and economics. Classical formulations, however, generally ignore capacity limits that are intrinsic in…
The Schr\"odinger bridge problem (SBP) seeks to find the measure $\hat{\mathbf{P}}$ on a certain path space which interpolates between state-space distributions $\rho_0$ at time $0$ and $\rho_T$ at time $T$ while minimizing the KL…
The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability…
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…
This work establishes a framework for solving inverse boundary problems with the geodesic based quadratic Wasserstein distance ($W_{2}$). A general form of the Fr\'echet gradient is systematically derived by optimal transportation (OT)…
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…
We study optimal transport (OT) problem for probability measures supported on a tree metric space. It is known that such OT problem (i.e., tree-Wasserstein (TW)) admits a closed-form expression, but depends fundamentally on the underlying…
The paper studies the optimal density steering problem for nonlinear continuous-time stochastic systems. To accurately capture nonlinear dynamics in high-uncertainty regions that deviate significantly from a nominal linearization point, we…
We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows…
Statistical mechanics is a powerful framework for analyzing optimization yielding analytical results for matching, optimal transport, and other combinatorial problems. However, these methods typically target the zero-temperature limit,…
Computational optimal transport (OT) has recently emerged as a powerful framework with applications in various fields. In this paper we focus on a relaxation of the original OT problem, the entropic OT problem, which allows to implement…
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…
Variational problems that involve Wasserstein distances and more generally optimal transport (OT) theory are playing an increasingly important role in data sciences. Such problems can be used to form an examplar measure out of various…
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…