Related papers: Spread Flows for Manifold Modelling

The analysis of data sets arising from multiple sensors has drawn significant research attention over the years. Traditional methods, including kernel-based methods, are typically incapable of capturing nonlinear geometric structures. We…

Streamflow, as a natural phenomenon, is continuous in time and so are the meteorological variables which influence its variability. In practice, it can be of interest to forecast the whole flow curve instead of points (daily or hourly). To…

Modern generative modeling methods have demonstrated strong performance in learning complex data distributions from clean samples. In many scientific and imaging applications, however, clean samples are unavailable, and only noisy or…

Symmetry is fundamental to understanding physical systems and can improve performance and sample efficiency in machine learning. Both pursuits require knowledge of the underlying symmetries in data, yet discovering these symmetries…

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,…

The blooming diffusion probabilistic models (DPMs) have garnered significant interest due to their impressive performance and the elegant inspiration they draw from physics. While earlier DPMs relied upon the Markovian assumption, recent…

A fundamental problem in manifold learning is to approximate a functional relationship in a data chosen randomly from a probability distribution supported on a low dimensional sub-manifold of a high dimensional ambient Euclidean space. The…

The ability to represent and compare machine learning models is crucial in order to quantify subtle model changes, evaluate generative models, and gather insights on neural network architectures. Existing techniques for comparing data…

In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…

Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…

Foundational language models show a remarkable ability to learn new concepts during inference via context data. However, similar work for images lag behind. To address this challenge, we introduce FLoWN, a flow matching model that learns to…

In recent years there has been increased interest in understanding the interplay between deep generative models (DGMs) and the manifold hypothesis. Research in this area focuses on understanding the reasons why commonly-used DGMs succeed or…

Sampling from unnormalized densities is analogous to the generative modeling problem, but the target distribution is defined by a known energy function instead of data samples. Because evaluating the energy function is often costly, a…

A machine learning method to predict steady external fluid flows using elliptic input features is introduced. Using data from as few as one high-fidelity simulation, the proposed method produces models generalizable under changes to…

Continuous diffusion has been the foundation of high-fidelity, controllable, and few-step generation of many data modalities such as images. However, in language modeling, prior continuous diffusion language models (DLMs) lag behind…

This paper presents a novel framework for aligning learnable latent spaces to arbitrary target distributions by leveraging flow-based generative models as priors. Our method first pretrains a flow model on the target features to capture the…

Learning the distribution of data on Riemannian manifolds is crucial for modeling data from non-Euclidean space, which is required by many applications in diverse scientific fields. Yet, existing generative models on manifolds suffer from…

This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…

Since its foundations, more than one hundred years ago, the field of structural biology has strived to understand and analyze the properties of molecules and their interactions by studying the structure that they take in 3D space. However,…

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…