Related papers: Fisher Flow Matching for Generative Modeling over …

Data heterogeneity hinders clinical deployment of medical image analysis models, and generative data augmentation helps mitigate this issue. However, recent diffusion-based methods that synthesize image-mask pairs often ignore distribution…

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…

This paper proposes a novel method, Explicit Flow Matching (ExFM), for training and analyzing flow-based generative models. ExFM leverages a theoretically grounded loss function, ExFM loss (a tractable form of Flow Matching (FM) loss), to…

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…

Discrete Diffusion Language Models progressed rapidly as an alternative to autoregressive (AR) models, motivated by their parallel generation abilities. However, for tractability, discrete diffusion models sample from a factorized…

Flow-based Generative Models (FGMs) effectively transform noise into complex data distributions. Incorporating Optimal Transport (OT) to couple noise and data during FGM training has been shown to improve the straightness of flow…

Diffusion and flow-based models have become the state of the art for generative AI across a wide range of data modalities, including images, videos, shapes, molecules, music, and more. This tutorial provides a self-contained introduction to…

The Wasserstein-Fisher-Rao (WFR) metric extends dynamic optimal transport (OT) by coupling displacement with change of mass, providing a principled geometry for modeling unbalanced snapshot dynamics. Existing WFR solvers, however, are often…

Flow Matching has limited ability in achieving one-step generation due to its reliance on learned curved trajectories. Previous studies have attempted to address this limitation by either modifying the coupling distribution to prevent…

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…

Deep generative models such as flow and diffusion models have proven to be effective in modeling high-dimensional and complex data types such as videos or proteins, and this has motivated their use in different data modalities, such as…

Diffusion and flow-based models have become the de facto approaches for generating continuous data, e.g., in domains such as images and videos. Their success has attracted growing interest in applying them to language modeling. Unlike their…

Generating molecular graphs is crucial in drug design and discovery but remains challenging due to the complex interdependencies between nodes and edges. While diffusion models have demonstrated their potentiality in molecular graph design,…

In this paper, we propose RiemannianFlow, a deep generative model that allows robots to learn complex and stable skills evolving on Riemannian manifolds. Examples of Riemannian data in robotics include stiffness (symmetric and positive…

Continuous diffusion and flow matching models could represent a powerful alternative to autoregressive approaches for language modelling (LM), as they unlock a host of advantages currently reserved for continuous modalities, including…

Geometric data and purpose-built generative models on them have become ubiquitous in high-impact deep learning application domains, ranging from protein backbone generation and computational chemistry to geospatial data. Current geometric…

Although many deep-learning-based super-resolution approaches have been proposed in recent years, because no ground truth is available in the inference stage, few can quantify the errors and uncertainties of the super-resolved results. For…

We address the problem of data augmentation in a rotating turbulence set-up, a paradigmatic challenge in geophysical applications. The goal is to reconstruct information in two-dimensional (2D) cuts of the three-dimensional flow fields,…

Inferring physical fields from sparse observations while strictly satisfying partial differential equations (PDEs) is a fundamental challenge in computational physics. Recently, deep generative models offer powerful data-driven priors for…

In image restoration, single-step discriminative mappings often lack fine details via expectation learning, whereas generative paradigms suffer from inefficient multi-step sampling and noise-residual coupling. To address this dilemma, we…