Related papers: Generative Learning With Euler Particle Transport

We propose a \textbf{uni}fied \textbf{f}ramework for \textbf{i}mplicit \textbf{ge}nerative \textbf{m}odeling (UnifiGem) with theoretical guarantees by integrating approaches from optimal transport, numerical ODE, density-ratio…

We develop an Euler-type method to predict the evolution of a time-dependent probability measure without explicitly learning an operator that governs its evolution. We use linearized optimal transport theory to prove that the measure-valued…

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…

We propose the characteristic generator, a novel one-step generative model that combines the efficiency of sampling in Generative Adversarial Networks (GANs) with the stable performance of flow-based models. Our model is driven by…

Optimal Mass Transport (OMT) is a well studied problem with a variety of applications in a diverse set of fields ranging from Physics to Computer Vision and in particular Statistics and Data Science. Since the original formulation of Monge…

Motivated by the computational difficulties incurred by popular deep learning algorithms for the generative modeling of temporal densities, we propose a cheap alternative which requires minimal hyperparameter tuning and scales favorably to…

We introduceGraphGPT, a novel self-supervised generative pre-trained model for graph learning based on the Graph Eulerian Transformer (GET). First, we propose GET, which combines a standard transformer encoder or decoder architecture with…

We present a deep generative model, named Monge-Amp\`ere flow, which builds on continuous-time gradient flow arising from the Monge-Amp\`ere equation in optimal transport theory. The generative map from the latent space to the data space…

We study unsupervised generative modeling in terms of the optimal transport (OT) problem between true (but unknown) data distribution $P_X$ and the latent variable model distribution $P_G$. We show that the OT problem can be equivalently…

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 propose a machine-learning method for evaluating the potential barrier governing atomic transport based on the preferential selection of dominant points for the atomic transport. The proposed method generates numerous random samples of…

In this paper, we present a new ensemble-based filter method by reconstructing the analysis step of the particle filter through a transport map, which directly transports prior particles to posterior particles. The transport map is…

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…

In light of the recent advancements in machine learning, we propose a novel approach to neutron source distribution estimation through the utilisation of probabilistic generative models. The estimation is based on a Monte Carlo particle…

We investigate the problem of sampling from posterior distributions with intractable normalizing constants in Bayesian inference. Our solution is a new generative modeling approach based on optimal transport (OT) that learns a deterministic…

Modern generative models are usually designed to match target distributions directly in the data space, where the intrinsic dimension of data can be much lower than the ambient dimension. We argue that this discrepancy may contribute to the…

Generative modelling is a key tool in unsupervised machine learning which has achieved stellar success in recent years. Despite this huge success, even the best generative models such as Generative Adversarial Networks (GANs) and…

Popular generative model learning methods such as Generative Adversarial Networks (GANs), and Variational Autoencoders (VAE) enforce the latent representation to follow simple distributions such as isotropic Gaussian. In this paper, we…

High-dimensional generative modeling is fundamentally a manifold-learning problem: real data concentrate near a low-dimensional structure embedded in the ambient space. Effective generators must therefore balance support fidelity -- placing…

This paper addresses the practical challenge in Entropic Optimal Transport (EOT) where the underlying ground cost function is typically latent and unobserved. Rather than assuming a fixed geometric cost, we adopt a data-driven approach…