Related papers: Schr\"odinger bridge based deep conditional genera…
Denoising diffusion models have recently emerged as a powerful class of generative models. They provide state-of-the-art results, not only for unconditional simulation, but also when used to solve conditional simulation problems arising in…
We consider the problem of sampling from an unknown distribution for which only a sufficiently large number of training samples are available. Such settings have recently drawn considerable interest in the context of generative modelling…
We propose to learn a generative model via entropy interpolation with a Schr\"{o}dinger Bridge. The generative learning task can be formulated as interpolating between a reference distribution and a target distribution based on the…
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…
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…
This paper aims to conduct a comprehensive theoretical analysis of current diffusion models. We introduce a novel generative learning methodology utilizing the Schr{\"o}dinger bridge diffusion model in latent space as the framework for…
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…
We study generative modeling for time series using entropic optimal transport and the Schr\"odinger bridge (SB) framework, with a focus on applications in finance and energy modeling. Extending the diffusion-based approach of Hamdouche,…
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),…
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…
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…
The dynamic Schr\"odinger bridge problem seeks a stochastic process that defines a transport between two target probability measures, while optimally satisfying the criteria of being closest, in terms of Kullback-Leibler divergence, to a…
Recently, diffusion-based generative models have demonstrated remarkable performance in speech enhancement tasks. However, these methods still encounter challenges, including the lack of structural information and poor performance in low…
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 proposes a generative speech enhancement model based on Schr\"odinger bridge (SB). The proposed model is employing a tractable SB to formulate a data-to-data process between the clean speech distribution and the observed noisy…
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…
Recently, a series of papers proposed deep learning-based approaches to sample from target distributions using controlled diffusion processes, being trained only on the unnormalized target densities without access to samples. Building on…
Generative diffusion models use time-forward and backward stochastic differential equations to connect the data and prior distributions. While conventional diffusion models (e.g., score-based models) only learn the backward process, more…
We propose a deep generative approach to sampling from a conditional distribution based on a unified formulation of conditional distribution and generalized nonparametric regression function using the noise-outsourcing lemma. The proposed…
We introduce an ordinary differential equation (ODE) based deep generative method for learning conditional distributions, named Conditional F\"ollmer Flow. Starting from a standard Gaussian distribution, the proposed flow could approximate…