Related papers: Convergence analysis of OT-Flow for sample generat…
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…
Recent studies suggest utilizing generative models instead of traditional auto-regressive algorithms for time series forecasting (TSF) tasks. These non-auto-regressive approaches involving different generative methods, including GAN,…
Optimal Transport (OT) based distances are powerful tools for machine learning to compare probability measures and manipulate them using OT maps. In this field, a setting of interest is semi-discrete OT, where the source measure $\mu$ is…
We present theoretical convergence guarantees for ODE-based generative models, specifically flow matching. We use a pre-trained autoencoder network to map high-dimensional original inputs to a low-dimensional latent space, where a…
We investigate the semi-discrete Optimal Transport (OT) problem, where a continuous source measure $\mu$ is transported to a discrete target measure $\nu$, with particular attention to the OT map approximation. In this setting, Stochastic…
Flow matching has emerged as a powerful framework for generative modeling, offering computational advantages over diffusion models by leveraging deterministic Ordinary Differential Equations (ODEs) instead of stochastic dynamics. While…
The ability to compare two degenerate probability distributions (i.e. two probability distributions supported on two distinct low-dimensional manifolds living in a much higher-dimensional space) is a crucial problem arising in the…
Flow Matching (FM) generative models offer efficient simulation-free training and deterministic sampling, but their practical deployment is challenged by high-precision parameter requirements. We adapt optimal transport (OT)-based…
Optimal transport (OT) theory provides a principled framework for modeling mass movement in applications such as mobility, logistics, and economics. Classical formulations, however, generally ignore capacity limits that are intrinsic in…
We provide a theoretical analysis for end-to-end training Discrete Flow Matching (DFM) generative models. DFM is a promising discrete generative modeling framework that learns the underlying generative dynamics by training a neural network…
We study the estimation of optimal transport (OT) maps between an arbitrary source probability measure and a log-concave target probability measure. Our contributions are twofold. First, we propose a new evolution equation in the set of…
Flow matching has recently emerged as a promising alternative to diffusion-based generative models, offering faster sampling and simpler training by learning continuous flows governed by ordinary differential equations. Despite growing…
We reformulate Optimal Transport Conditional Flow Matching (OT-CFM), a class of dynamical generative models, showing that it admits an exact proximal formulation via an extended Brenier potential, without assuming that the target…
Flow-based Generative Models (FGMs) effectively transform noise into complex data distributions. Incorporating Optimal Transport (OT) to couple noise and data during FGM training has been shown to improve the straightness of flow…
Diffusion and flow matching models generate samples by learning time-dependent vector fields whose integration transports noise to data, requiring tens to hundreds of network evaluations at inference. We instead learn the transport map…
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…
Over the several recent years, there has been a boom in development of Flow Matching (FM) methods for generative modeling. One intriguing property pursued by the community is the ability to learn flows with straight trajectories which…
Deep generative models provide state-of-the-art performance across a wide array of applications, with recent studies showing increasing applicability for science and engineering. Despite a growing corpus of literature focused on the…
Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…
A normalizing flow is an invertible mapping between an arbitrary probability distribution and a standard normal distribution; it can be used for density estimation and statistical inference. Computing the flow follows the change of…