Related papers: BM$^2$: Coupled Schr\"{o}dinger Bridge Matching
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…
Monitoring bridge health using vibrations of drive-by vehicles has various benefits, such as no need for directly installing and maintaining sensors on the bridge. However, many of the existing drive-by monitoring approaches are based on…
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…
Attention mechanisms, particularly channel attention, have become highly influential in numerous computer vision tasks. Despite their effectiveness, many existing methods primarily focus on optimizing performance through complex attention…
We investigate the martingale Schr\"odinger bridge, recently introduced by Nutz and Wiesel as a distinguished martingale transport plan between two probability measures in convex order. We show that this construction extends naturally to…
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,…
Generative models offer a direct way of modeling complex data. Energy-based models attempt to encode the statistical correlations observed in the data at the level of the Boltzmann weight associated with an energy function in the form of a…
The unbalanced Schr\"odinger bridge problem (uSBP) seeks to interpolate between a probability measure $\rho_0$ and a sub-probability measure $\rho_T$ while minimizing KL divergence to a reference measure $\mathbf{R}$ on a path space. In…
We present Fractional Diffusion Bridge Models (FDBM), a novel generative diffusion bridge framework driven by an approximation of the rich and non-Markovian fractional Brownian motion (fBM). Real stochastic processes exhibit a degree of…
This paper addresses the design of transmit precoder and receive combiner matrices to support $N_{\rm s}$ independent data streams over a time-division duplex (TDD) point-to-point massive multiple-input multiple-output (MIMO) channel with…
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…
Diffusion models have risen to prominence in time series forecasting, showcasing their robust capability to model complex data distributions. However, their effectiveness in deterministic predictions is often constrained by instability…
Deep Ensemble (DE) approach is a straightforward technique used to enhance the performance of deep neural networks by training them from different initial points, converging towards various local optima. However, a limitation of this…
Flow Matching (FM) (also referred to as stochastic interpolants or rectified flows) stands out as a class of generative models that aims to bridge in finite time the target distribution $\nu^\star$ with an auxiliary distribution $\mu$,…
We consider transport over a strongly connected, directed graph. The scheduling amounts to selecting transition probabilities for a discrete-time Markov evolution which is designed to be consistent with certain initial and final marginals.…
Multiscale problems can usually be approximated through numerical homogenization by an equation with some effective parameters that can capture the macroscopic behavior of the original system on the coarse grid to speed up the simulation.…
This paper exploit the equivalence between the Schr\"odinger Bridge problem and the entropy penalized optimal transport in order to find a different approach to the duality, in the spirit of optimal transport. This approach results in a…
Machine learning-based unfolding has enabled unbinned and high-dimensional differential cross section measurements. Two main approaches have emerged in this research area: one based on discriminative models and one based on generative…
Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called ``bridges''), is investigated theoretically by analyzing discrete-state stochastic ``burnt-bridge'' models. When an…
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…