Related papers: Diffusion model for the time evolution of particle…

We perform numerical simulations to examine particle diffusion at steady shear in a model granular material in two dimensions at the jamming density and zero temperature. We confirm findings by others that the diffusion constant depends on…

Diffusion models have demonstrated strong generative performance; however, generated samples often fail to fully align with human intent. This paper studies a test-time scaling method that enables sampling from regions with higher…

We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of…

Denoising diffusion models represent a recent emerging topic in computer vision, demonstrating remarkable results in the area of generative modeling. A diffusion model is a deep generative model that is based on two stages, a forward…

Taylor's model of dispersion simply describes the long-term spread of material along a pipe, channel or river. However, often we need multi-mode models to resolve finer details in space and time. Here we construct zonal models of dispersion…

Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…

The coupling between advection and diffusion in position space can often lead to enhanced mass transport compared to diffusion without flow. An important framework used to characterize the long-time diffusive transport in position space is…

The performance of optimization-based robot motion planning algorithms is highly dependent on the initial solutions, commonly obtained by running a sampling-based planner to obtain a collision-free path. However, these methods can be slow…

This book presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward…

We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum co-ordinate vary freely and restrict only angle with…

We study a one dimensional generalization of the exponential trap model using both numerical simulations and analytical approximations. We obtain the asymptotic shape of the average diffusion front in the sub-diffusive phase. Our central…

We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…

This paper introduces the use of statistical distributions based on transport differential equations for clear distinction of transport modes within transient kinetic experiments. More specifically,novel techniques are developed for the…

Deep generative models learn the data distribution, which is concentrated on a low-dimensional manifold. The geometric analysis of distribution transformation provides a better understanding of data structure and enables a variety of…

Discrete flow models offer a powerful framework for learning distributions over discrete state spaces and have demonstrated superior performance compared to the discrete diffusion models. However, their convergence properties and error…

Superdiffusive transport with dynamical exponent $z=3/2$ has been firmly established at finite temperature for a class of integrable systems with a non-abelian global symmetry $G$. On the inclusion of integrability-breaking perturbations,…

Translational diffusion coefficients are routinely estimated from molecular dynamics simulations. Linear fits to mean squared displacement (MSD) curves have become the de facto standard, from simple liquids to complex biomacromolecules.…

We analyze deterministic and random temporal variations in dispersion measure (DM) from the full three-dimensional velocities of pulsars with respect to the solar system, combined with electron-density variations on a wide range of length…

Diffusion models have emerged as a powerful framework in generative modeling, typically relying on optimizing neural networks to estimate the score function via forward SDE simulations. In this work, we propose an alternative method that is…

A constructive approach to theory of diffusion processes is proposed, which is based on application of both the symmetry analysis and method of modelling functions. An algorithm for construction of the modelling functions is suggested. This…