相关论文: Deep Generalized Schr\"odinger Bridges: From Image…

Mean-Field Game (MFG) serves as a crucial mathematical framework in modeling the collective behavior of individual agents interacting stochastically with a large population. In this work, we aim at solving a challenging class of MFGs in…

Modern distribution matching algorithms for training diffusion or flow models directly prescribe the time evolution of the marginal distributions between two boundary distributions. In this work, we consider a generalized distribution…

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…

Score-based generative models have recently attracted significant attention for their ability to generate high-fidelity data by learning maps from simple Gaussian priors to complex data distributions. A natural generalization of this idea…

Schrodinger Bridges (SBs) are diffusion processes that steer, in finite time, a given initial distribution to another final one while minimizing a suitable cost functional. Although various methods for computing SBs have recently been…

Transportation on graphs is a fundamental challenge across many domains, where decisions must respect topological and operational constraints. Despite the need for actionable policies, existing graph-transport methods lack this…

Schr\"odinger Bridge (SB) is an entropy-regularized optimal transport problem that has received increasing attention in deep generative modeling for its mathematical flexibility compared to the Scored-based Generative Model (SGM). However,…

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 Quantum Schr\"odinger Bridge Problem (QSBP) describes the evolution of a stochastic process between two arbitrary probability distributions, where the dynamics are governed by the Schr\"odinger equation rather than by the traditional…

Diffusion Schr\"odinger bridges (DSB) have recently emerged as a powerful framework for recovering stochastic dynamics via their marginal observations at different time points. Despite numerous successful applications, existing algorithms…

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…

Schr\"odinger bridges (SBs) provide an elegant framework for modeling the temporal evolution of populations in physical, chemical, or biological systems. Such natural processes are commonly subject to changes in population size over time…

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),…

Transporting between arbitrary distributions is a fundamental goal in generative modeling. Recently proposed diffusion bridge models provide a potential solution, but they rely on a joint distribution that is difficult to obtain in…

Compared to the existing function-based models in deep generative modeling, the recently proposed diffusion models have achieved outstanding performance with a stochastic-process-based approach. But a long sampling time is required for this…

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…

We demonstrate the versatility of mean-field games (MFGs) as a mathematical framework for explaining, enhancing, and designing generative models. In generative flows, a Lagrangian formulation is used where each particle (generated sample)…

We introduce a novel training principle for probabilistic models that is an alternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework is based on learning the transition operator of a Markov chain whose…

Generating samples from a probability distribution is a fundamental task in machine learning and statistics. This article proposes a novel scheme for sampling from a distribution for which the probability density $\mu({\bf x})$ for ${\bf…

We study Diffusion Schr\"odinger Bridge (DSB) models in the context of dynamical astrophysical systems, specifically tackling observational inverse prediction tasks within Giant Molecular Clouds (GMCs) for star formation. We introduce the…