Related papers: $\alpha$-Flow: A Unified Framework for Continuous-…

Dense image correspondence is central to many applications, such as visual odometry, 3D reconstruction, object association, and re-identification. Historically, dense correspondence has been tackled separately for wide-baseline scenarios…

In order to prevent velocity, pressure, and temperature spikes at material discontinuities occurring when the interface-capturing schemes inconsistently simulate compressible multi-material flows(when the specific heats ratio is…

We study Flow Matching in a semi-discrete setting where a Gaussian source is transported toward a discrete target supported on finitely many points. This semi-discrete regime is the theoretical setting behind the use of Flow Matching for…

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…

The generation of 3D molecules requires simultaneously deciding the categorical features~(atom types) and continuous features~(atom coordinates). Deep generative models, especially Diffusion Models (DMs), have demonstrated effectiveness in…

Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative…

Generative models based on dynamical equations such as flows and diffusions offer exceptional sample quality, but require computationally expensive numerical integration during inference. The advent of consistency models has enabled…

Training deep neural networks remains computationally intensive due to the itera2 tive nature of gradient-based optimization. We propose Gradient Flow Matching (GFM), a continuous-time modeling framework that treats neural network training…

In contexts where data samples represent a physically stable state, it is often assumed that the data points represent the local minima of an energy landscape. In control theory, it is well-known that energy can serve as an effective…

Flow matching casts sample generation as learning a continuous-time velocity field that transports noise to data. Existing flow matching networks typically predict each point's velocity independently, considering only its location and time…

We present Functional Mean Flow (FMF) as a one-step generative model defined in infinite-dimensional Hilbert space. FMF extends the one-step Mean Flow framework to functional domains by providing a theoretical formulation for Functional…

Maximum flow (and minimum cut) algorithms have had a strong impact on computer vision. In particular, graph cuts algorithms provide a mechanism for the discrete optimization of an energy functional which has been used in a variety of…

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…

Flow based generative models have charted an impressive path across multiple visual generation tasks by adhering to a simple principle: learning velocity representations of a linear interpolant. However, we observe that training velocity…

This paper introduces a novel generative model for discrete distributions based on continuous normalizing flows on the submanifold of factorizing discrete measures. Integration of the flow gradually assigns categories and avoids issues of…

Graph generative models are essential across diverse scientific domains by capturing complex distributions over relational data. Among them, graph diffusion models achieve superior performance but face inefficient sampling and limited…

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…

Flow matching has emerged as a powerful framework for generative modeling, with recent empirical successes highlighting the effectiveness of signal-space prediction ($x$-prediction). In this work, we investigate the transfer of this…

Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different…

Existing rectified flow models are based on linear trajectories between data and noise distributions. This linearity enforces zero curvature, which can inadvertently force the image generation process through low-probability regions of the…