Related papers: Time-inhomogeneous diffusion geometry and topology
We seek to give users precise control over diffusion-based image generation by modeling complex scenes as sequences of layers, which define the desired spatial arrangement and visual attributes of objects in the scene. Collage Diffusion…
Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in…
Diffusion-based inpainting can reconstruct missing image areas with high quality from sparse data, provided that their location and their values are well optimised. This is particularly useful for applications such as image compression,…
Geological parameterization entails the representation of a geomodel using a small set of latent variables and a mapping from these variables to grid-block properties such as porosity and permeability. Parameterization is useful for data…
Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by…
Topology and machine learning are two actively researched topics not only in condensed matter physics, but also in data science. Here, we propose the use of topological data analysis in unsupervised learning of the topological phase…
Diffusion models have been central to the development of recent image, video, and even text generation systems. They posses striking geometric properties that can be faithfully portrayed in low-dimensional settings. However, existing…
Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…
Diffusion models excel at creating visually impressive images but often struggle to generate images with a specified topology. The Betti number, which represents the number of structures in an image, is a fundamental measure in topology.…
Diffusion-based manifold learning methods have proven useful in representation learning and dimensionality reduction of modern high dimensional, high throughput, noisy datasets. Such datasets are especially present in fields like biology…
The growth by condensation of small water droplets in a three-dimensional homogeneous isotropic turbulent flow is considered. Within a simple model of advection and condensation, the dynamics and growth of millions of droplets are…
This paper introduces a comprehensive unified framework for constructing multi-view diffusion geometries through intertwined multi-view diffusion trajectories (MDTs), a class of inhomogeneous diffusion processes that iteratively combine the…
We present an novel framework for efficiently and effectively extending the powerful continuous diffusion processes to discrete modeling. Previous approaches have suffered from the discrepancy between discrete data and continuous modeling.…
Video inpainting is the task of filling a region in a video in a visually convincing manner. It is very challenging due to the high dimensionality of the data and the temporal consistency required for obtaining convincing results. Recently,…
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…
Diffusion models have become the go-to method for many generative tasks, particularly for image-to-image generation tasks such as super-resolution and inpainting. Current diffusion-based methods do not provide statistical guarantees…
Spatial profiling technologies in biology, such as imaging mass cytometry (IMC) and spatial transcriptomics (ST), generate high-dimensional, multi-channel data with strong spatial alignment and complex inter-channel relationships.…
Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…
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…
We develop an information-theoretic approach to isoperimetric inequalities based on entropy dissipation under heat flow. By viewing diffusion as a noisy information channel, we measure how mutual information about set membership decays over…