Related papers: Diffusion approximation for noise-induced evolutio…
We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted "onion-shell" geometry bounded by two nested membranes of…
Diffusion models have been shown to implicitly generate visual content autoregressively in the frequency domain, where low-frequency components are generated earlier in the denoising process while high-frequency details emerge only in later…
Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models,…
The long time behavior of an absorbed Markov process is well described by the limiting distribution of the process conditioned to not be killed when it is observed. Our aim is to give an approximation's method of this limit, when the…
To understand the effect of assortative mating on the genetic evolution of a population, we consider a finite population in which each individual has a type, determined by a sequence of n diallelic loci. We assume that the population…
Initial fluctuations in hydrodynamic fields such as energy density or flow velocity give access to understanding initial state and equilibration physics as well as thermodynamic and transport properties. We provide evidence that the fluid…
Motion prediction is a challenging problem in autonomous driving as it demands the system to comprehend stochastic dynamics and the multi-modal nature of real-world agent interactions. Diffusion models have recently risen to prominence, and…
We propose a generalized diffusion equation for a flat Euclidean space subjected to a continuous infinitesimal scale transform. For the special cases of an algebraic or exponential expansion/contraction, governed by time-dependent scale…
Models of diffusion driven pattern formation that rely on the Turing mechanism are utilized in many areas of science. However, many such models suffer from the defect of requiring fine tuning of parameters or an unrealistic separation of…
We consider stochastic diffusion processes absorbed at the boundary of a domain. It is shown that there exist initial distributions which ensure a given decreasing of density of the absorbed process.
We investigate the statistical and computational limits of latent Diffusion Transformers (DiTs) under the low-dimensional linear latent space assumption. Statistically, we study the universal approximation and sample complexity of the DiTs…
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,…
In the present paper we discuss the modifications introduced into the first-order Fermi shock acceleration process due to a finite extent of diffusive regions near the shock or due to boundary conditions leading to an increased particle…
Single-molecule localization microscopy allows practitioners to locate and track labeled molecules in biological systems. When extracting diffusion coefficients from the resulting trajectories, it is common practice to perform a linear fit…
Starting from the dynamical system model capturing the splitting-differentiation process of populations, we extend this notion to show how the speciation mechanism from a single species leads to the consideration of several well known…
Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…
This paper is concerned with stochastic reaction-diffusion kinetics governed by the reaction-diffusion master equation. Specifically, the primary goal of this paper is to provide a mechanistic basis of Turing pattern formation that is…
Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…
We consider the general problem of the first passage distribution of particles whose displacements are subject to time delays. We show that this problem gives rise to a \emph{propagation-dispersion equation} which is obtained as the…
Diffusion condensation is a dynamic process that yields a sequence of multiscale data representations that aim to encode meaningful abstractions. It has proven effective for manifold learning, denoising, clustering, and visualization of…