Related papers: An accurate, fast, mathematically robust, universa…
Diffusion models (DMs) have been adopted across diverse fields with its remarkable abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a stochastic…
This paper proposes a robust fast multi-band image fusion method to merge a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. Following the method recently developed in [1], the generalized…
We approximate a diffusion equation with highly oscillatory coefficients with a diffusion equation with constant coefficients. The approach is put in action in contexts where only partial information (namely the global energy stored in the…
In this paper, we study the problem of computing the effective diffusivity for particles moving in chaotic flows. Instead of solving a convection-diffusion type cell problem in the Eulerian formulation (arising from homogenization theory…
A low diffusive flux difference splitting based kinetic scheme is developed based on a discrete velocity Boltzmann equation, with a novel three velocity model. While two discrete velocities are used for upwinding, the third discrete…
We study a fully discrete finite element method for variable-order time-fractional diffusion equations with a time-dependent variable order. Optimal convergence estimates are proved with the first-order accuracy in time (and second order…
Reaction-diffusion problems are often described at a macroscopic scale by partial derivative equations of the type of the Fisher or Kolmogorov-Petrovsky-Piscounov equation. These equations have a continuous family of front solutions, each…
This study introduces a novel point-wise diffusion model that processes spatio-temporal points independently to efficiently predict complex physical systems with shape variations. This methodological contribution lies in applying forward…
Considering a real-valued diffusion, a real-valued reward function and a positive discount rate, we provide an algorithm to solve the optimal stopping problem consisting in finding the optimal expected discounted reward and the optimal…
Bulk matter produced in heavy ion collisions has multiple conserved quantum numbers like baryon number, strangeness and electric charge. The diffusion process of these charges can be described by a diffusion matrix describing the…
Inspired by random walk on graphs, diffusion map (DM) is a class of unsupervised machine learning that offers automatic identification of low-dimensional data structure hidden in a high-dimensional dataset. In recent years, among its many…
Schrodinger Bridges (SBs) are diffusion processes that steer, in finite time, a given initial distribution to another final one while minimizing a suitable cost functional. Although various methods for computing SBs have recently been…
We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the…
Markov chain Monte Carlo samplers based on discretizations of (overdamped) Langevin dynamics are commonly used in the Bayesian inference and computational statistical physics literature to estimate high-dimensional integrals. One can…
In this paper we study the problem of the numerical calculation (by Monte Carlo Methods) of the effective diffusivity for a particle moving in a periodic divergent-free velocity filed, in the limit of vanishing molecular diffusion. In this…
Many monostable reaction-diffusion equations admit one-dimensional travelling waves if and only if the wave speed is sufficiently high. The values of these minimum wave speeds are not known exactly, except in a few simple cases. We present…
Diffusion inversion is the problem of taking an image and a text prompt that describes it and finding a noise latent that would generate the exact same image. Most current deterministic inversion techniques operate by approximately solving…
Score-based diffusion models, which generate new data by learning to reverse a diffusion process that perturbs data from the target distribution into noise, have achieved remarkable success across various generative tasks. Despite their…
We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…
Diffusion models have achieved impressive success in high-fidelity image generation but suffer from slow sampling due to their inherently iterative denoising process. While recent one-step methods accelerate inference by learning direct…