Related papers: Generalised Flow Maps for Few-Step Generative Mode…

Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much distort relationships between points, i.e. pairwise distances…

One-step generative modeling seeks to generate high-quality data samples in a single function evaluation, significantly improving efficiency over traditional diffusion or flow-based models. In this work, we introduce Modular MeanFlow (MMF),…

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…

Generating high-dimensional visual modalities is a computationally intensive task. A common solution is progressive generation, where the outputs are synthesized in a coarse-to-fine spectral autoregressive manner. While diffusion models…

Large or very large spatial (and spatio-temporal) datasets have become common place in many environmental and climate studies. These data are often collected in non-Euclidean spaces (such as the planet Earth) and they often present…

Generative Flow Networks (GFNs) were initially introduced on directed acyclic graphs to sample from an unnormalized distribution density. Recent works have extended the theoretical framework for generative methods allowing more flexibility…

We introduce Random Projection Flows (RPFs), a principled framework for injective normalizing flows that leverages tools from random matrix theory and the geometry of random projections. RPFs employ random semi-orthogonal matrices, drawn…

Generative models have emerged as a powerful paradigm for solving physics systems and modeling complex spatiotemporal dynamics. However, achieving high physical accuracy without incurring high computational cost remains a fundamental…

Recent diffusion and flow matching models have demonstrated strong capabilities in image generation and editing by progressively removing noise through iterative sampling. While this enables flexible inversion for semantic-preserving edits,…

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…

In this paper, we propose a randomized generalized multiscale finite element method (Randomized GMsFEM) for flow problems with parameterized inputs and high-contrast heterogeneous media. The method employs a data-driven predictor to…

Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical…

Flow matching models have shown great potential in image generation tasks among probabilistic generative models. However, most flow matching models in the literature do not explicitly utilize the underlying clustering structure in the…

Graph generation is a fundamental task with wide applications in modeling complex systems. Although existing methods align the spectrum or degree profile of the target graph, they often ignore the geometry induced by eigenvectors and the…

We propose Riemannian Denoising Diffusion Probabilistic Models (RDDPMs) for learning distributions on submanifolds of Euclidean space that are level sets of functions, including most of the manifolds relevant to applications. Existing…

Learning mappings between functional spaces, also known as function-on-function regression, is a fundamental problem in functional data analysis with broad applications, including spatiotemporal forecasting, curve prediction, and climate…

Urban wind flow modeling and simulation play an important role in air quality assessment and sustainable city planning. A key challenge for modeling and simulation is handling the complex geometries of the urban landscape. Low order models…

This work introduces the Grassmannian Diffusion Maps, a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the…

Gaussian processes (GPs) are very widely used for modeling of unknown functions or surfaces in applications ranging from regression to classification to spatial processes. Although there is an increasingly vast literature on applications,…

Simulating the long-time evolution of Hamiltonian systems is limited by the small timesteps required for stable numerical integration. To overcome this constraint, we introduce a framework to learn Hamiltonian Flow Maps by predicting the…