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Generative models aim to learn the distribution of datasets, such as images, so as to be able to generate samples that statistically resemble real data. However, learning the underlying probability distribution can be very challenging and…

Generative AI (GenAI) has revolutionized data-driven modeling by enabling the synthesis of high-dimensional data across various applications, including image generation, language modeling, biomedical signal processing, and anomaly…

Generative Adversarial Networks (GANs) can produce high-quality samples, but do not provide an estimate of the probability density around the samples. However, it has been noted that maximizing the log-likelihood within an energy-based…

Diffusion models and flow-based methods have shown impressive generative capability, especially for images, but their sampling is expensive because it requires many iterative updates. We introduce W-Flow, a framework for training a…

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…

In this paper, we propose a new and unified approach for nonparametric regression and conditional distribution learning. Our approach simultaneously estimates a regression function and a conditional generator using a generative learning…

We introduce a novel unit-time ordinary differential equation (ODE) flow called the preconditioned F\"{o}llmer flow, which efficiently transforms a Gaussian measure into a desired target measure at time 1. To discretize the flow, we apply…

Generative Adversarial Networks (GANs) are one of the most practical methods for learning data distributions. A popular GAN formulation is based on the use of Wasserstein distance as a metric between probability distributions.…

Generative Adversarial Networks (GANs) have shown immense potential in fields such as text and image generation. Only very recently attempts to exploit GANs to statistical-mechanics models have been reported. Here we quantitatively test…

Computing optimal transport maps between high-dimensional and continuous distributions is a challenging problem in optimal transport (OT). Generative adversarial networks (GANs) are powerful generative models which have been successfully…

Generative modeling over discrete structures underpins applications across deep learning, from biological sequence design and code generation to large language models, yet generation often remains sequential, relying on autoregressive…

Sampling conditional distributions is a fundamental task for Bayesian inference and density estimation. Generative models, such as normalizing flows and generative adversarial networks, characterize conditional distributions by learning a…

Generating high-fidelity time series data using generative adversarial networks (GANs) remains a challenging task, as it is difficult to capture the temporal dependence of joint probability distributions induced by time-series data. Towards…

We propose \emph{Euler Mean Flows (EMF)}, a flow-based generative framework for one-step and few-step generation that enforces long-range trajectory consistency with minimal sampling cost. The key idea of EMF is to replace the trajectory…

We introduce three new generative models for time series that are based on Euler discretization of Stochastic Differential Equations (SDEs) and Wasserstein metrics. Two of these methods rely on the adaptation of generative adversarial…

Learning probabilistic models that can estimate the density of a given set of samples, and generate samples from that density, is one of the fundamental challenges in unsupervised machine learning. We introduce a new generative model based…

Conditional distribution is a fundamental quantity for describing the relationship between a response and a predictor. We propose a Wasserstein generative approach to learning a conditional distribution. The proposed approach uses a…

Score-based generative models have emerged as a powerful approach for sampling high-dimensional probability distributions. Despite their effectiveness, their theoretical underpinnings remain relatively underdeveloped. In this work, we study…

Recently, flow-based generative models have shown superior efficiency compared to diffusion models. In this paper, we study rectified flow models, which constrain transport trajectories to be linear from the base distribution to the data…

This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples. Our main results establish the convergence rates of GANs under a collection of integral probability metrics defined…