Related papers: Time-inhomogeneous diffusion geometry and topology

What is the "right" topological invariant of a large point cloud X? Prior research has focused on estimating the full persistence diagram of X, a quantity that is very expensive to compute, unstable to outliers, and far from a sufficient…

Diffusion and flow matching models have unlocked unprecedented capabilities for creative content creation, such as interactive image and streaming video generation. The growing demand for higher resolutions, frame rates, and context…

Topology can extract the structural information in a dataset efficiently. In this paper, we attempt to incorporate topological information into a multiple output Gaussian process model for transfer learning purposes. To achieve this goal,…

We study a data-dependent notion of diffusion-model generalization: when a model does not memorize the training set, where do its generated samples go relative to the geometry induced by the data? To answer this, we introduce a…

Diffusion models typically generate data through a fixed denoising trajectory that is shared across all samples. However, generation targets can differ in complexity, suggesting that a single pre-defined diffusion process may not be optimal…

Recent empirical studies have demonstrated that diffusion models can effectively learn the image distribution and generate new samples. Remarkably, these models can achieve this even with a small number of training samples despite a large…

A diffusion probabilistic model (DPM), which constructs a forward diffusion process by gradually adding noise to data points and learns the reverse denoising process to generate new samples, has been shown to handle complex data…

Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of…

We introduce Diffusion Active Learning, a novel approach that combines generative diffusion modeling with data-driven sequential experimental design to adaptively acquire data for inverse problems. Although broadly applicable, we focus on…

Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…

Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…

The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…

Diffusion-based voxel prior modelling is challenging for the reconstruction of large-scale 3D porous microstructures. Due to the demanding requirements for simultaneously modelling both the continuous pore morphology and the discrete…

Diffusion models, though originally designed for generative tasks, have demonstrated impressive self-supervised representation learning capabilities. A particularly intriguing phenomenon in these models is the emergence of unimodal…

We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…

High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…

Diffusion generative models transform noise into data by inverting a process that progressively adds noise to data samples. Inspired by concepts from the renormalization group in physics, which analyzes systems across different scales, we…

Recently, diffusion models have made remarkable progress in text-to-image (T2I) generation, synthesizing images with high fidelity and diverse contents. Despite this advancement, latent space smoothness within diffusion models remains…

In this paper, we study the problem of using representation learning to assist information diffusion prediction on graphs. In particular, we aim at estimating the probability of an inactive node to be activated next in a cascade. Despite…

We propose a new class of generative models that naturally handle data of varying dimensionality by jointly modeling the state and dimension of each datapoint. The generative process is formulated as a jump diffusion process that makes…