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Flow matching has emerged as a powerful framework for generative modeling through continuous normalizing flows. We investigate a potential topological constraint: when the prior distribution and target distribution have mismatched topology…
Statistical surrogate modeling of fluid flows is hard because dynamics are multiscale and highly sensitive to initial conditions. Conditional diffusion surrogates can be accurate, but usually need hundreds of stochastic sampling steps. We…
Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate…
Flow matching has recently emerged as a flexible and efficient framework for generative modelling by learning deterministic transport dynamics between probability measures. In this work, we extend flow matching to the space of probability…
This paper introduces for the first time a framework to obtain provable worst-case guarantees for neural network performance, using learning for optimal power flow (OPF) problems as a guiding example. Neural networks have the potential to…
Flow matching (FM) learns vector fields by regressing stochastic velocity targets along intermediate distributions $p_t$. We identify a geometric optimization bottleneck in this regression problem: when the covariance $\Sigma_t$ of $p_t$ is…
Unconditional flow-matching trains diffusion models to transport samples from a source distribution to a target distribution by enforcing that the flows between sample pairs are unique. However, in conditional settings (e.g.,…
Learning probabilistic surrogates for partial differential equations remains challenging in data-scarce regimes: neural operators require large amounts of high-fidelity data, while generative approaches typically sacrifice resolution…
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…
Score-based generative modeling with probability flow ordinary differential equations (ODEs) has achieved remarkable success in a variety of applications. While various fast ODE-based samplers have been proposed in the literature and…
Flow Matching has become a cornerstone of modern generative models like Stable Diffusion 3, largely due to the efficiency of its Rectified Flow (RF) variant. The success of RF hinges on iteratively learning straight trajectories, pushing…
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,…
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…
Flow Matching and Transformer architectures have demonstrated remarkable performance in image generation tasks, with recent work FlowAR [Ren et al., 2024] synergistically integrating both paradigms to advance synthesis fidelity. However,…
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 the domain of computer vision, optical flow stands as a cornerstone for unraveling dynamic visual scenes. However, the challenge of accurately estimating optical flow under conditions of large nonlinear motion patterns remains an open…
Fast flow models accelerate the iterative sampling process by learning to directly predict ODE path integrals, enabling one-step or few-step generation. However, we argue that current fast-flow training paradigms suffer from two fundamental…
Score-based diffusion models have become a foundational paradigm for modern generative modeling, demonstrating exceptional capability in generating samples from complex high-dimensional distributions. Despite the dominant adoption of…
This paper introduces Gauge Flow Models, a novel class of Generative Flow Models. These models incorporate a learnable Gauge Field within the Flow Ordinary Differential Equation (ODE). A comprehensive mathematical framework for these…
Generative modeling typically concerns transporting a single source distribution to a target distribution via simple probability flows. However, in fields like computer graphics and single-cell genomics, samples themselves can be viewed as…