Related papers: Diffusion maps, spectral clustering and reaction c…

We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised…

Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…

Medical image segmentation is a challenging task, made more difficult by many datasets' limited size and annotations. Denoising diffusion probabilistic models (DDPM) have recently shown promise in modelling the distribution of natural…

We discuss the problem of extending data mining approaches to cases in which data points arise in the form of individual graphs. Being able to find the intrinsic low-dimensionality in ensembles of graphs can be useful in a variety of…

Low-dimensional dynamical systems are fruitful models for mixing in fluid and granular flows. We study a one-dimensional discontinuous dynamical system (termed "cutting and shuffling" of a line segment), and we present a comprehensive…

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…

Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…

Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…

Consistency models have been proposed for fast generative modeling, achieving results competitive with diffusion and flow models. However, these methods exhibit inherent instability and limited reproducibility when training from scratch,…

The unsupervised learning of community structure, in particular the partitioning vertices into clusters or communities, is a canonical and well-studied problem in exploratory graph analysis. However, like most graph analyses the…

Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or…

With the emergence of Artificial Intelligence, numerical algorithms are moving towards more approximate approaches. For methods such as PCA or diffusion maps, it is necessary to compute eigenvalues of a large matrix, which may also be dense…

In Diffusion Probabilistic Models (DPMs), the task of modeling the score evolution via a single time-dependent neural network necessitates extended training periods and may potentially impede modeling flexibility and capacity. To counteract…

Deep generative models have made rapid progress in image, text, audio, and video generation, and are increasingly being applied to structured records. For tabular data, however, generative modeling remains difficult: a dataset may contain…

Dimension reduction techniques usually lose information in the sense that reconstructed data are not identical to the original data. However, we argue that it is possible to have reconstructed data identically distributed as the original…

Diffusion models have become a leading framework in generative modeling, yet their theoretical understanding -- especially for high-dimensional data concentrated on low-dimensional structures -- remains incomplete. This paper investigates…

Dataset distillation aims to synthesize a compact subset of the original data, enabling models trained on it to achieve performance comparable to those trained on the original large dataset. Existing distribution-matching methods are…

Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations…

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…