Related papers: Time-inhomogeneous diffusion geometry and topology

Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…

Clustering $\unicode{x2013}$ the tendency for neighbors of nodes to be connected $\unicode{x2013}$ quantifies the coupling of a complex network to its latent metric space. In random geometric graphs, clustering undergoes a continuous phase…

Dataset condensation aims to condense a large dataset with a lot of training samples into a small set. Previous methods usually condense the dataset into the pixels format. However, it suffers from slow optimization speed and large number…

Diffusion models generate high-dimensional data such as images by learning a process that gradually removes noise from corrupted data. Recent studies have shown that the backward dynamics of diffusion models exhibit two characteristic…

Can continuous diffusion models bring the same performance breakthrough on natural language they did for image generation? To circumvent the discrete nature of text data, we can simply project tokens in a continuous space of embeddings, as…

For domains that involve numerical simulation, it can be computationally expensive to run an ensemble of simulations spanning a parameter space of interest to a user. To this end, an attractive surrogate for simulation is the generative…

We use a Convolutional Recurrent Neural Network approach to learn morphological evolution driven by surface diffusion. To this aim we first produce a training set using phase field simulations. Intentionally, we insert in such a set only…

We propose a method called integrated diffusion for combining multimodal datasets, or data gathered via several different measurements on the same system, to create a joint data diffusion operator. As real world data suffers from both local…

Extensive numerical simulation are reported for the structure and dynamics of large clusters on metal(100) surfaces. Different types of perimeter hopping processes makes center-of-mass of the cluster to follow a a random walk trajectory.…

Diffusion models have emerged as a promising alternative to autoregressive models in modeling discrete categorical data. However, diffusion models that directly work on discrete data space fail to fully exploit the power of iterative…

Geometric evolution represents a fundamental aspect of many physical phenomena. In this paper we consider the geometric evolution of structures that undergo topological changes. Topological changes occur when the shape of an object evolves…

A central problem in data analysis is the low dimensional representation of high dimensional data, and the concise description of its underlying geometry and density. In the analysis of large scale simulations of complex dynamical systems,…

We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local…

Diffusion models are loosely modelled based on non-equilibrium thermodynamics, where \textit{diffusion} refers to particles flowing from high-concentration regions towards low-concentration regions. In statistics, the meaning is quite…

Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional…

Diffusion models have attracted significant attention due to the remarkable ability to create content and generate data for tasks like image classification. However, the usage of diffusion models to generate the high-quality object…

Topological data analysis asks when balls in a metric space $(X,d)$ intersect. Geometric data analysis asks how much balls have to be enlarged to intersect. We connect this principle to the traditional core geometric concept of curvature.…

Diffusion guidance is a powerful technique that enables controllable and high-fidelity sample generation with diffusion models. At a high level, it modifies the score function by incorporating a guidance term that steers the generative…

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…

Do contemporary diffusion models preserve the class geometry of hyperspherical data? Standard diffusion models rely on isotropic Gaussian noise in the forward process, inherently favoring Euclidean spaces. However, many real-world problems…