Related papers: Diffusion Geometry
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…
This paper studies the problem of distributed Riemannian optimization over a network of agents whose cost functions are geodesically smooth but possibly geodesically non-convex. Extending a well-known distributed optimization strategy…
We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet…
We introduce a new methodology for forecasting which we call Signal Diffusion Mapping. Our approach accommodates features of real world financial data which have been ignored historically in existing forecasting methodologies. Our method…
We develop a diffusion-based approach for various document layout sequence generation. Layout sequences specify the contents of a document design in an explicit format. Our novel diffusion-based approach works in the sequence domain rather…
In this work, we address two major issues in recent Denoising Diffusion Probabilistic Models (DDPM): {\bf 1)} geometric key feature extraction and {\bf 2)} network equivariance. Since the DDPM prediction network relies on the U-net…
Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…
In this work, we propose a novel framework for estimating the dimension of the data manifold using a trained diffusion model. A diffusion model approximates the score function i.e. the gradient of the log density of a noise-corrupted…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
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…
This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes 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…
This paper lays the foundations for a unified framework for numerically and computationally applying methods drawn from a range of currently distinct geometrical approaches to statistical modelling. In so doing, it extends information…
Imaging systems are represented as linear operators, and their singular value spectra describe the structure recoverable at the operator level. Building on an operator-based information-theoretic framework, this paper introduces a minimal…
The gradient discretisation method (GDM) is a generic framework for designing and analysing numerical schemes for diffusion models. In this paper, we study the GDM for the porous medium equation, including fast diffusion and slow diffusion…
Data scarcity hinders deep learning for medical imaging. We propose a framework for breast cancer classification in thermograms that addresses this using a Diffusion Probabilistic Model (DPM) for data augmentation. Our DPM-based…
Diffusion has emerged as a powerful framework for generative modeling, achieving remarkable success in applications such as image and audio synthesis. Enlightened by this progress, we propose a novel diffusion-based approach for symbolic…
This introductory text arises from a lecture given in G\"oteborg, Sweden, given by the first author and is intended for undergraduate students, as well as for any mathematically inclined reader wishing to explore a synthesis of ideas…
Generative models have recently undergone significant advancement due to the diffusion models. The success of these models can be often attributed to their use of guidance techniques, such as classifier or classifier-free guidance, which…
Diffusion generative models have demonstrated remarkable success in visual domains such as image and video generation. They have also recently emerged as a promising approach in robotics, especially in robot manipulations. Diffusion models…