Related papers: Flow Matching: Markov Kernels, Stochastic Processe…

This paper presents a groundbreaking approach to causal inference by integrating continuous normalizing flows (CNFs) with parametric submodels, enhancing their geometric sensitivity and improving upon traditional Targeted Maximum Likelihood…

Discrete flow models offer a powerful framework for learning distributions over discrete state spaces and have demonstrated superior performance compared to the discrete diffusion models. However, their convergence properties and error…

We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…

Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals with non-smooth Riesz kernels show a rich structure as singular measures can become absolutely continuous ones and conversely. In this paper we contribute to the…

We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…

Modeling the transport dynamics of natural processes from population-level observations is a ubiquitous problem in the natural sciences. Such models rely on key assumptions about the underlying process in order to enable faithful learning…

Traditional discriminative computer vision relies predominantly on static projections, mapping input features to outputs in a single computational step. Although efficient, this paradigm lacks the iterative refinement and robustness…

The conventional understanding of adversarial training in generative adversarial networks (GANs) is that the discriminator is trained to estimate a divergence, and the generator learns to minimize this divergence. We argue that despite the…

This paper presents a novel method for accelerating path-planning tasks in unknown scenes with obstacles by utilizing Wasserstein Generative Adversarial Networks (WGANs) with Gradient Penalty (GP) to approximate the distribution of…

Numerous biological and physical processes can be modeled as systems of interacting entities evolving continuously over time, e.g. the dynamics of communicating cells or physical particles. Learning the dynamics of such systems is essential…

Flow and bridge matching are a novel class of processes which encompass diffusion models. One of the main aspect of their increased flexibility is that these models can interpolate between arbitrary data distributions i.e. they generalize…

Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…

Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients (or initial states) and…

Velocity autocorrelation functions (VAF) of the fluids are studied on short- and long-time scales within a unified approach. This approach is based on an effective summation of the infinite continued fraction at a reasonable assumption…

A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing…

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…

Guidance of generative models is typically achieved by modifying the probability flow vector field through the addition of a guidance field. In this paper, we instead propose the Source-Guided Flow Matching (SGFM) framework, which modifies…

Continuous normalizing flows (CNFs) are a generative method for learning probability distributions, which is based on ordinary differential equations. This method has shown remarkable empirical success across various applications, including…

We introduce in this paper new and very effective numerical methods based on neural networks for the approximation of the mean curvature flow of either oriented or non-orientable surfaces. To learn the correct interface evolution law, our…

We prove existence and uniqueness of solutions to a transport equation modelling vehicular traffic in which the velocity field depends non-locally on the downstream traffic density via a discontinuous anisotropic kernel. The result is…