Related papers: A scheme for simulating one-dimensional diffusion …
Diffusion models are the current state-of-the-art in image generation, synthesizing high-quality images by breaking down the generation process into many fine-grained denoising steps. Despite their good performance, diffusion models are…
The dynamics of a freely diffusing particle in a two-dimensional channel with cross sectional area $A(x)$, can be effectively described by a one-dimensional diffusion equation under the action of a potential of mean force $U(x)=-k_BT\ln…
This paper presents a new numerical scheme for simulating stochastic processes specified by their marginal distribution functions and covariance functions. Stochastic samples are firstly generated to automatically satisfy target marginal…
Originating from the diffusion phenomenon in physics that describes particle movement, the diffusion generative models inherit the characteristics of stochastic random walk in the data space along the denoising trajectory. However, the…
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…
A system of interacting Brownian particles subject to short-range repulsive potentials is considered. A continuum description in the form of a nonlinear diffusion equation is derived systematically in the dilute limit using the method of…
In this paper, we present a theoretical and computational workflow for the non-parametric Bayesian inference of drift and diffusion functions of autonomous diffusion processes. We base the inference on the partial differential equations…
Kinetic equations model the position-velocity distribution of particles subject to transport and collision effects. Under a diffusive scaling, these combined effects converge to a diffusion equation for the position density in the limit of…
It is demonstrated that the description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach previously used in the literature is shown to…
Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…
Diffusion rates through a membrane can be asymmetric, if the diffusing particles are spatially extended and the pores in the membrane have asymmetric structure. This phenomenon is demonstrated here via a deterministic simulation of a…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
We reconsider the problem of diffusion of particles at constant speed and present a generalization of the Telegrapher process to higher dimensional stochastic media ($d>1$), where the particle can move along $2^d$ directions. We derive the…
Score-based diffusion models (SBDM) have recently emerged as state-of-the-art approaches for image generation. Existing SBDMs are typically formulated in a finite-dimensional setting, where images are considered as tensors of finite size.…
We describe a new, surprisingly simple algorithm, that simulates exact sample paths of a class of stochastic differential equations. It involves rejection sampling and, when applicable, returns the location of the path at a random…
Dissipative particle dynamics (DPD) is now a well-established method for simulating soft matter systems. However, its applicability was recently questioned because some investigations showed an upper coarse-graining limit that would prevent…
The problem of diffusion in a porous medium with a spatially varying porosity is considered. The particular microstructure analyzed comprises a collection of impenetrable spheres, though the methods developed are general. Two different…
A result is given to find points where a real valued function on the plane is not smooth. Provided this function is induced by a smooth mapping from three dimensions to the plane, from a function on surfaces in three dimensions. This has…
In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…
Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic…