Related papers: Diffusion Bridge Mixture Transports, Schr\"odinger…
Solving inverse problems -- recovering signals from incomplete or noisy measurements -- is fundamental in science and engineering. Score-based generative models (SGMs) have recently emerged as a powerful framework for this task. Two main…
Image-to-image translation is an important and challenging problem in computer vision and image processing. Diffusion models (DM) have shown great potentials for high-quality image synthesis, and have gained competitive performance on the…
Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative…
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…
Diffusion models demonstrate remarkable capabilities in capturing complex data distributions and have achieved compelling results in many generative tasks. While they have recently been extended to dense prediction tasks such as depth…
Diffusion-based generative models have achieved promising results recently, but raise an array of open questions in terms of conceptual understanding, theoretical analysis, algorithm improvement and extensions to discrete, structured,…
Generalized Schr\"odinger Bridges (GSBs) are a fundamental mathematical framework used to analyze the most likely particle evolution based on the principle of least action including kinetic and potential energy. In parallel to their…
The Mean-Field Schrodinger Bridge (MFSB) problem is an optimization problem aiming to find the minimum effort control policy to drive a McKean-Vlassov stochastic differential equation from one probability measure to another. In the context…
This paper motivates the use of random-bridges -- stochastic processes conditioned to take target distributions at fixed timepoints -- in the realm of generative modelling. Herein, random-bridges can act as stochastic transports between two…
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…
Computed tomography (CT) is a cornerstone imaging modality for non-invasive, high-resolution visualization of internal anatomical structures. However, when the scanned object exceeds the scanner's field of view (FOV), projection data are…
This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…
Entropy-regularized optimal transport, which has strong links to the Schr\"odinger bridge problem in statistical mechanics, enjoys a variety of applications from trajectory inference to generative modeling. A major driver of renewed…
Generative diffusion models, famous for their performance in image generation, are popular in various cross-domain applications. However, their use in the communication community has been mostly limited to auxiliary tasks like data modeling…
The Schr\"odinger bridge problem (SBP) aims at finding the measure $\hat{\mathbf{P}}$ on a certain path space which possesses the desired state-space distributions $\rho_0$ at time $0$ and $\rho_T$ at time $T$ while minimizing the KL…
Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it.…
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…
Recent advances in generative modeling have positioned diffusion models as state-of-the-art tools for sampling from complex data distributions. While these models have shown remarkable success across single-modality domains such as images…
Quantum counterparts of Schrodinger's classical bridge problem have been around for the better part of half a century. During that time, several quantum approaches to this multifaceted classical problem have been introduced. In the present…
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.…