相关论文: Diffusion & Adversarial Schr\"odinger Bridges via …

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

The Schr\"odinger eigenvalue problem is solved with the imaginary time propagation technique. The separability of the Hamiltonian makes the problem suitable for the application of splitting methods. High order fractional time steps of order…

Homotopy approaches to Bayesian inference have found widespread use especially if the Kullback-Leibler divergence between the prior and the posterior distribution is large. Here we extend one of these homotopy approach to include an…

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…

The convergence properties of the Iterative water-filling (IWF) based algorithms have been derived in the ideal situation where the transmitters in the network are able to obtain the exact value of the interference plus noise (IPN)…

The efficient resolution of Bayesian inverse problems remains challenging due to the high computational cost of traditional sampling methods. In this paper, we propose a novel framework that integrates Conditional Flow Matching (CFM) with a…

Diffusion models have been successful in learning complex data distributions. This capability has driven their application to high-dimensional multi-objective black-box optimization problem. Existing approaches often employ an external…

Nonnegative matrix factorization (NMF), which is the approximation of a data matrix as the product of two nonnegative matrices, is a key issue in machine learning and data analysis. One approach to NMF is to formulate the problem as a…

Motivated by applications in trajectory inference and particle tracking, we introduce Smooth Schr\"odinger Bridges. Our proposal generalizes prior work by allowing the reference process in the Schr\"odinger Bridge problem to be a smooth…

Given two boundary distributions, the Schr\"odinger Bridge (SB) problem seeks the ``most likely`` random evolution between them with respect to a reference process. It has revealed rich connections to recent machine learning methods for…

We present a parallel version of the well-known Split-Step Fourier method (SSF) for solving the Nonlinear Schr\"odinger equation, a mathematical model describing wave packet propagation in fiber optic lines. The algorithm is implemented…

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…

The purpose of the present work is to expand substantially the type of control and estimation problems that can be addressed following the paradigm of Schr\"odinger bridges, by incorporating termination (killing) of stochastic flows.…

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…

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 iterative proportional fitting procedure, introduced in 1937 by Kruithof, aims to adjust the elements of an array to satisfy specified row and column sums. Given a rectangular non-negative matrix $X_0$ and two positive marginals $a$ and…

Diffuse interface descriptions offer many advantages for the modeling of microstructure evolution. However, the numerical representation of moving diffuse interfaces on discrete numerical grids involves spurious grid friction, which limits…

This paper develops and analyzes a general iterative framework for solving parameter-dependent and random convection-diffusion problems. It is inspired by the multi-modes method of [7,8] and the ensemble method of [20] and extends those…

Sampling from unnormalized densities using diffusion models has emerged as a powerful paradigm. However, while recent approaches that use least-squares `matching' objectives have improved scalability, they often necessitate significant…

The optimal mass transport problem gives a geometric framework for optimal allocation, and has recently gained significant interest in application areas such as signal processing, image processing, and computer vision. Even though it can be…