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We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate in infinite-dimensional spaces. Our approach works by first defining a path of probability…

Path planning in complex environments is one of the key problems of artificial intelligence because it requires simultaneous understanding of the geometry of space and the global structure of the problem. In this paper, we explore the…

Flow Matching (FM) is a recent framework for generative modeling that has achieved state-of-the-art performance across various domains, including image, video, audio, speech, and biological structures. This guide offers a comprehensive and…

With the rapid advancement of diffusion-based generative models, portrait image animation has achieved remarkable results. However, it still faces challenges in temporally consistent video generation and fast sampling due to its iterative…

We reveal a precise mathematical framework about a new family of generative models which we call Gradient Flow Drifting. With this framework, we prove an equivalence between the recently proposed Drifting Model and the Wasserstein gradient…

Diffusion model (DM)-based channel estimation, which generates channel samples via a posteriori sampling stepwise with denoising process, has shown potential in high-precision channel state information (CSI) acquisition. However, slow…

Pre-training has been investigated to improve the efficiency and performance of training neural operators in data-scarce settings. However, it is largely in its infancy due to the inherent complexity and diversity, such as long…

A generative model capable of sampling realistic molecules with desired properties could accelerate chemical discovery across a wide range of applications. Toward this goal, significant effort has focused on developing models that jointly…

Denoising-based models, such as diffusion and flow matching, have been a critical component of robotic manipulation for their strong distribution-fitting and scaling capacity. Concurrently, several works have demonstrated that simple…

Large Reasoning Models (LRMs) excel at complex reasoning tasks, but their efficiency is often hampered by overly verbose outputs. Prior steering methods attempt to address this issue by applying a single, global vector to hidden…

Generative models such as diffusion and flow matching have become dominant paradigms for visuomotor policy learning, yet their reliance on iterative denoising incurs high inference latency incompatible with real-time robotic control. We…

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…

Flow matching and diffusion bridge models have emerged as leading paradigms in generative speech enhancement, modeling stochastic processes between paired noisy and clean speech signals based on principles such as flow matching, score…

Diffusion-based generative models have achieved state-of-the-art performance for perceptual quality in speech enhancement (SE). However, their iterative nature requires numerous Neural Function Evaluations (NFEs), posing a challenge for…

Diffusion models have achieved significant progress in both image and video generation while still suffering from huge computation costs. As an effective solution, flow matching aims to reflow the diffusion process of diffusion models into…

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…

We propose a framework for probabilistic forecasting of dynamical systems based on generative modeling. Given observations of the system state over time, we formulate the forecasting problem as sampling from the conditional distribution of…

Recent studies suggest utilizing generative models instead of traditional auto-regressive algorithms for time series forecasting (TSF) tasks. These non-auto-regressive approaches involving different generative methods, including GAN,…

Generative models, particularly Diffusion Models (DM), have shown strong potential for Computed Tomography (CT) reconstruction serving as expressive priors for solving ill-posed inverse problems. However, diffusion-based reconstruction…

Generative modeling can be formulated as learning a mapping f such that its pushforward distribution matches the data distribution. The pushforward behavior can be carried out iteratively at inference time, for example in diffusion and…