Related papers: A Generalized Sinkhorn Algorithm for Mean-Field Sc…
We present simulation-free score and flow matching ([SF]$^2$M), a simulation-free objective for inferring stochastic dynamics given unpaired samples drawn from arbitrary source and target distributions. Our method generalizes both the…
In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…
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…
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…
Diffusion in heterogeneous media partitioned by semi-permeable interfaces has a wide range of applications in the physical and life sciences, including gas permeation in soils, diffusion magnetic resonance imaging (dMRI), drug delivery,…
We consider inference (filtering) problems over probabilistic graphical models with aggregate data generated by a large population of individuals. We propose a new efficient belief propagation type algorithm over tree-structured graphs with…
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 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…
We propose Image-to-Image Schr\"odinger Bridge (I$^2$SB), a new class of conditional diffusion models that directly learn the nonlinear diffusion processes between two given distributions. These diffusion bridges are particularly useful for…
We propose a novel generative model for time series based on Schr{\"o}dinger bridge (SB) approach. This consists in the entropic interpolation via optimal transport between a reference probability measure on path space and a target measure…
Diffusion-based planning has achieved strong results in single-agent offline reinforcement learning, yet scaling to many-agent systems remains intractable due to the curse of dimensionality in the joint trajectory space. We introduce…
In recent years, reinforcement learning and its multi-agent analogue have achieved great success in solving various complex control problems. However, multi-agent reinforcement learning remains challenging both in its theoretical analysis…
In this work, we consider one-dimensional particles interacting in mean-field type through a bounded kernel. In addition, when particles hit some barrier (say zero), they are removed from the system. This absorption of particles is…
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…
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…
The solution of the path structured multimarginal Schr\"{o}dinger bridge problem (MSBP) is the most-likely measure-valued trajectory consistent with a sequence of observed probability measures or distributional snapshots. We leverage recent…
Mean-field control (MFC) offers a scalable solution to the curse of dimensionality in multi-agent systems but traditionally hinges on the restrictive assumption of exchangeability via dense, all-to-all interactions. In this work, we bridge…
For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…
The framework of Mean-field Games (MFGs) is used for modelling the collective dynamics of large populations of non-cooperative decision-making agents. We formulate and analyze a kinetic MFG model for an interacting system of non-cooperative…
We introduce the concept of {\it mean-field optimal control} which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional…