Related papers: Diffusion Maps meet Nystr\"om
Kernel mean embeddings are a powerful tool to represent probability distributions over arbitrary spaces as single points in a Hilbert space. Yet, the cost of computing and storing such embeddings prohibits their direct use in large-scale…
Text-to-image diffusion models have demonstrated unprecedented capabilities for flexible and realistic image synthesis. Nevertheless, these models rely on a time-consuming sampling procedure, which has motivated attempts to reduce their…
In this work, we present a novel convolutional neural net- work based method for perfusion map generation in dynamic suscepti- bility contrast-enhanced perfusion imaging. The proposed architecture is trained end-to-end and solely relies on…
Map makers have long searched for a way to construct cartograms -- maps in which the sizes of geographic regions such as countries or provinces appear in proportion to their population or some other analogous property. Such maps are…
We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…
Accurate environmental representations are essential for autonomous driving, providing the foundation for safe and efficient navigation. Traditionally, high-definition (HD) maps are providing this representation of the static road…
We discuss a diffusion based implementation of the self-organizing map on the unit hypersphere. We show that this approach can be efficiently implemented using just linear algebra methods, we give a python numpy implementation, and we…
Denoising Diffusion Models (DDMs) have become a popular tool for generating high-quality samples from complex data distributions. These models are able to capture sophisticated patterns and structures in the data, and can generate samples…
Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of…
We introduce the concept of Hypoelliptic Diffusion Maps (HDM), a framework generalizing Diffusion Maps in the context of manifold learning and dimensionality reduction. Standard non-linear dimensionality reduction methods (e.g., LLE,…
In this paper, we point out that suboptimal noise-data mapping leads to slow training of diffusion models. During diffusion training, current methods diffuse each image across the entire noise space, resulting in a mixture of all images at…
The application of the diffusion in many computer vision and artificial intelligence projects has been shown to give excellent improvements in performance. One of the main bottlenecks of this technique is the quadratic growth of the kNN…
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…
This paper explores the application diffusion maps as graph shift operators in understanding the underlying geometry of graph signals. The study evaluates the improvements in graph learning when using diffusion map generated filters to the…
Embedding large graphs in low dimensional spaces has recently attracted significant interest due to its wide applications such as graph visualization, link prediction and node classification. Existing methods focus on computing the…
In this paper we investigate a sub-diffusion equation for simulating the anomalous diffusion phenomenon in real physical environment. Based on an equivalent transformation of the original sub-diffusion equation followed by the use of a…
Diffusion models represent a powerful family of generative models widely used for image and video generation. However, the time-consuming deployment, long inference time, and requirements on large memory hinder their applications on…
Diffusion models have recently achieved remarkable performance in image super-resolution (SR), but their high computational cost limits practical deployment in remote sensing applications. To address this issue, we propose SlimDiffSR, a…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
A method is proposed for the calculation of diffusion constants for one-dimensional maps exhibiting deterministic diffusion. The procedure is based on harmonic inversion and uses a known relation between the diffusion constant and the…