Related papers: The Long Time Limit of Diffusion Means
Denoising diffusion models are a recent class of generative models exhibiting state-of-the-art performance in image and audio synthesis. Such models approximate the time-reversal of a forward noising process from a target distribution to a…
Mathematical models of diffusive transport underpin our understanding of chemical, biochemical and biological transport phenomena. Analysis of such models often focusses on relatively simple geometries and deals with diffusion through…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
Score-based diffusion models are a highly effective method for generating samples from a distribution of images. We consider scenarios where the training data comes from a noisy version of the target distribution, and present an efficiently…
We investigate the information-theoretical limits of inference tasks in epidemic spreading on graphs in the thermodynamic limit. The typical inference tasks consist in computing observables of the posterior distribution of the epidemic…
Diffusion models have demonstrated remarkable empirical success in the recent years and are considered one of the state-of-the-art generative models in modern AI. These models consist of a forward process, which gradually diffuses the data…
Lateral diffusion of molecules on surfaces plays a very important role in various biological processes, including lipid transport across the cell membrane, synaptic transmission and other phenomena such as exo- and endocytosis, signal…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
Diffusion has been widely used to describe a random walk of particles or waves, and it requires only one parameter -- the diffusion constant. For waves, however, diffusion is an approximation that disregards the possibility of interference.…
Distribution function is essential in statistical inference, and connected with samples to form a directed closed loop by the correspondence theorem in measure theory and the Glivenko-Cantelli and Donsker properties. This connection creates…
Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…
An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media…
We demonstrate a new near-analytical path to the threshold-size of random-lasing for the case of a uniform and isotropic-scattering sphere. We assess a geometric-distribution-probability (GDP) weighted integration of the diffusion-equation…
Despite the success of diffusion models (DMs), we still lack a thorough understanding of their latent space. To understand the latent space $\mathbf{x}_t \in \mathcal{X}$, we analyze them from a geometrical perspective. Our approach…
We consider diffraction at random point scatterers on general discrete point sets in $\R^\nu$, restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate the speed of convergence…
We show that a unified and maximally generalized approach to spatial transformation design is possible, one that encompasses all second order waves, rays, and diffusion processes in anisotropic media. Until the final step, it is unnecessary…
Diffusion is the result of repeated random scattering. It governs a wide range of phenomena from Brownian motion, to heat flow through window panes, neutron flux in fuel rods, dispersion of light in human tissue, and electronic conduction.…
We study a diffusion approximation for a model of stochastic motion of a particle in one spatial dimension. The velocity of the particle is constant but the direction of the motion undergoes random changes with a Poisson clock. Moreover,…
This paper focuses on the time-harmonic electromagnetic (EM) scattering problem in a general medium which may possess a nontrivial topological structure. We model this by an inhomogeneous and possibly anisotropic medium with embedded…
Uncertainty quantification is critical in scientific inverse problems to distinguish identifiable parameters from those that remain ambiguous given available measurements. The Conditional Diffusion Model-based Inverse Problem Solver (CDI)…