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

We study the Schr\"odinger bridge problem when the endpoint distributions are available only through samples. Classical computational approaches estimate Schr\"odinger potentials via Sinkhorn iterations on empirical measures and then…

The Entropic Optimal Transport (EOT) problem and its dynamic counterpart, the Schr\"odinger bridge (SB) problem, play an important role in modern machine learning, linking generative modeling with optimal transport theory. While recent…

While diffusion-based image restoration (IR) methods have achieved remarkable success, they are still limited by the low inference speed attributed to the necessity of executing hundreds or even thousands of sampling steps. Existing…

We present an entirely new geometric and probabilistic approach to synchronization of correspondences across multiple sets of objects or images. In particular, we present two algorithms: (1) Birkhoff-Riemannian L-BFGS for optimizing the…

Diffusion models are a powerful class of generative models which simulate stochastic differential equations (SDEs) to generate data from noise. While diffusion models have achieved remarkable progress, they have limitations in unpaired…

Implicit generative modeling (IGM) aims to produce samples of synthetic data matching the characteristics of a target data distribution. Recent work (e.g. score-matching networks, diffusion models) has approached the IGM problem from the…

A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…

We consider the Schr\"odinger bridge problem which, given ensemble measurements of the initial and final configurations of a stochastic dynamical system and some prior knowledge on the dynamics, aims to reconstruct the "most likely"…

We study Markov processes generated by iterated function systems (IFS). The constituent maps of the IFS are monotonic transformations of the interval. We first obtain an upper bound on the number of SRB (Sinai-Ruelle-Bowen) measures for the…

We develop time integration methods in low-rank representation that can adaptively adjust approximation ranks to achieve a prescribed accuracy, while ensuring that these ranks remain proportional to the corresponding best approximation…

A space-time interface-fitted approximation of an inverse source problem for the advection-diffusion equation with moving subdomains is investigated. The problem is reformulated as an optimization problem using Tikhonov regularization. A…

An important problem in fiber-optic communications is to invert the nonlinear Schr\"odinger equation in real time to reverse the deterministic effects of the channel. Interestingly, the popular split-step Fourier method (SSFM) leads to a…

In this paper, we study the Schr\"odinger Bridge Problem (SBP), which is central to entropic optimal transport. For general reference processes and begin--endpoint distributions, we propose a forward-reverse iterative Monte Carlo procedure…

Typical iterated filters, such as the iterated extended Kalman filter (IEKF), iterated unscented Kalman filter (IUKF), and iterated posterior linearization filter (IPLF), have been developed to improve the linearization point (or density)…

We give a simple, multiplicative-weight update algorithm for learning undirected graphical models or Markov random fields (MRFs). The approach is new, and for the well-studied case of Ising models or Boltzmann machines, we obtain an…

At the core of modern generative modeling frameworks, including diffusion models, score-based models, and flow matching, is the task of transforming a simple prior distribution into a complex target distribution through stochastic paths in…

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…

The inverse source problem for the Helmholtz equation poses significant challenges, particularly when sources exhibit complex or discontinuous geometries. Traditional numerical methods suffer from prohibitive computational costs, while…

This study investigates the iterative refinement method applied to the solution of linear discrete inverse problems by considering its application to the Tikhonov problem in mixed precision. Previous works on mixed precision iterative…

Graphical models have found widespread applications in many areas of modern statistics and machine learning. Iterative Proportional Fitting (IPF) and its variants have become the default method for undirected graphical model estimation, and…