Related papers: Stable Autonomous Flow Matching

The success of deep generative models in generating high-quality and diverse samples is often attributed to particular architectures and large training datasets. In this paper, we investigate the impact of these factors on the quality and…

Strong semantic representations improve the convergence and generation quality of diffusion and flow models. Existing approaches largely rely on external models, which require separate training, operate on misaligned objectives, and exhibit…

High-dimensional count data arise in applications such as single-cell RNA sequencing and neural spike trains, where mapping between distributions across successive batches or time points form critical components of data analysis. The recent…

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…

Modern continuous-time generative models typically induce \emph{V-shaped} flows: each sample travels independently along a nearly straight trajectory from the prior to the data. Although effective, this independent movement overlooks the…

We consider stability analysis of constrained switching linear systems in which the dynamics is unknown and whose switching signal is constrained by an automaton. We propose a data-driven Lyapunov framework for providing probabilistic…

We propose a machine learning framework based on Flow Matching (FM) to identify critical properties in many-body systems efficiently. Using the 2D XY model as a benchmark, we demonstrate that a single network, trained only on configurations…

Generating high-quality time series data has emerged as a critical research topic due to its broad utility in supporting downstream time series mining tasks. A major challenge lies in modeling the intrinsic stochasticity of temporal…

Generative models that can model and predict sequences of future events can, in principle, learn to capture complex real-world phenomena, such as physical interactions. However, a central challenge in video prediction is that the future is…

Standard flow matching scales well but typically relies on an unstructured source distribution, limiting its ability to learn interpretable latent structure. Latent-variable models, by contrast, capture structure but often sacrifice…

While methods exist for aligning flow matching models--a popular and effective class of generative models--with human preferences, existing approaches fail to achieve both adaptation efficiency and probabilistically sound prior…

Flow Matching (FM) (also referred to as stochastic interpolants or rectified flows) stands out as a class of generative models that aims to bridge in finite time the target distribution $\nu^\star$ with an auxiliary distribution $\mu$,…

Flow matching has recently emerged as a powerful paradigm for generative modeling and has been extended to probabilistic time series forecasting in latent spaces. However, the impact of the specific choice of probability path model on…

Using a nonlocal second-order traffic flow model we present an approach to control the dynamics towards a steady state. The system is controlled by the leading vehicle driving at a prescribed velocity and also determines the steady state.…

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,…

We introduce Flux Matching, a new paradigm for generative modeling that generalizes existing score-based models to a broader family of vector fields that need not be conservative. Rather than requiring the model to equal the data score, the…

A curious phenomenon observed in some dynamical generative models is the following: despite learning errors in the score function or the drift vector field, the generated samples appear to shift \emph{along} the support of the data…

In this paper, we present a comprehensive theoretical comparison of diffusion and flow matching under the Generator Matching framework. Despite their apparent differences, both diffusion and flow matching can be viewed under the unified…

This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…

A valuable step in the modeling of multiscale dynamical systems in fields such as computational chemistry, biology, materials science and more, is the representative sampling of the phase space over long timescales of interest; this task is…