Related papers: Flow Matching with Semidiscrete Couplings
In this paper, we develop semidefinite programming (SDP) models aimed at solving optimal power flow (OPF) problems in distribution systems. We propose two models: the symmetrical SDP model which modifies the existing BFM-SDP model. Then…
Flow Matching (FM) has recently emerged as a leading approach for high-fidelity visual generation, offering a robust continuous-time alternative to ordinary differential equation (ODE) based models. However, despite their success, FM models…
Continuous normalizing flows (CNFs) construct invertible mappings between an arbitrary complex distribution and an isotropic Gaussian distribution using Neural Ordinary Differential Equations (neural ODEs). It has not been tractable on…
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…
Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent…
Diffusion and flow matching have emerged as expressive policy classes in reinforcement learning, but their reliance on multi-step denoising imposes substantial computational overhead at inference time, which is particularly problematic in…
Generating high-quality time-series data is challenging because real-world signals often exhibit multimodal patterns and multiscale dynamics, including oscillations and high-frequency variations. Flow Matching (FM) offers an efficient…
Optimal transport (OT) and Gromov-Wasserstein (GW) alignment are powerful frameworks for geometrically driven matching of probability distributions, yet their large-scale usage is hampered by high statistical and computational costs.…
An optimal transport (OT) problem seeks to find the cheapest mapping between two distributions with equal total density, given the cost of transporting density from one place to another. Unbalanced OT allows for different total density in…
Flow matching (FM) models extend ODE sampler based diffusion models into a general framework, significantly reducing sampling steps through learned vector fields. However, the theoretical understanding of FM models, particularly how their…
Generative target speaker extraction (TSE) methods often produce more natural outputs than predictive models. Recent work based on diffusion or flow matching (FM) typically relies on a small, fixed number of reverse steps with a fixed step…
Forecasting high-dimensional, PDE-governed dynamics remains a core challenge for generative modeling. Existing autoregressive and diffusion-based approaches often suffer cumulative errors and discretisation artifacts that limit long,…
Neural operator surrogates for time-dependent partial differential equations (PDEs) conventionally employ autoregressive prediction schemes, which accumulate error over long rollouts and require uniform temporal discretization. We introduce…
Flow matching trains a neural velocity field by regression against a target velocity associated with a prescribed probability path connecting a simple initial distribution to the data distribution. A central design choice is the path…
The bridge problem is to find an SDE (or sometimes an ODE) that bridges two given distributions. The application areas of the bridge problem are enormous, among which the recent generative modeling (e.g., conditional or unconditional image…
Optimal transport (OT) and maximum mean discrepancies (MMD) are now routinely used in machine learning to compare probability measures. We focus in this paper on \emph{Sinkhorn divergences} (SDs), a regularized variant of OT distances which…
Deep generative models aim to learn the underlying distribution of data and generate new ones. Despite the diversity of generative models and their high-quality generation performance in practice, most of them lack rigorous theoretical…
Simulating trajectories of dynamical systems is a fundamental problem in a wide range of fields such as molecular dynamics, biochemistry, and pedestrian dynamics. Machine learning has become an invaluable tool for scaling physics-based…
Despite Flow Matching and diffusion models having emerged as powerful generative paradigms for continuous variables such as images and videos, their application to high-dimensional discrete data, such as language, is still limited. In this…
Flow Matching (FM) policies have emerged as an efficient backbone for robotic control, offering fast and expressive action generation that underpins recent large-scale embodied AI systems. However, FM policies trained via imitation learning…