This paper proves a Krylov-Safonov estimate for a multidimensional diffusion process whose diffusion coefficients are degenerate on the boundary. As applications the existence and uniqueness of invariant probability measures for the process and Hoeld...
As a social media, online social networks play a vital role in the social information diffusion. However, due to its unique complexity, the mechanism of the diffusion in online social networks is different from the ones in other types of networks and...
The transport of charged particles in various astrophysical environments permeated by magnetic fields is described in terms of a diffusion process, which relies on diffusion-tensor parameters generally inferred from Monte-Carlo simulations. Based on...
We introduce and study a class of free boundary models with "nonlocal diffusion", which are natural extensions of the free boundary models in Du and Lin [17] and elsewhere, where "local diffusion" is used to describe the population dispersal, with th...
Generative models like diffusion and flow-matching create high-fidelity samples by progressively refining noise. The refinement process is notoriously slow, often requiring hundreds of function evaluations. We introduce Warm-Start Diffusion (WSD), a...
The problem of anomalous diffusion in the momentum space is considered on the basis of the appropriate probability transition function (PTF). New general equation for description of the diffusion of heavy particles in the gas of the light particles...
Stable Diffusion is a recent open-source image generation model comparable to proprietary models such as DALLE, Imagen, or Parti. Stable Diffusion comes with a safety filter that aims to prevent generating explicit images. Unfortunately, the filter i...
In this paper, we propose a novel coarse-to-fine continuous pose diffusion method to enhance the precision of pick-and-place operations within robotic manipulation tasks. Leveraging the capabilities of diffusion networks, we facilitate the accurate p...
In this paper we describe a learned method of traffic scene generation designed to simulate the output of the perception system of a self-driving car. In our "Scene Diffusion" system, inspired by latent diffusion, we use a novel combination of diffus...
We propose the Diffusion-Inversion-Net (DIN) framework for inverse modeling of groundwater flow and solute transport processes. DIN utilizes an offline-trained Denoising Diffusion Probabilistic Model (DDPM) as a powerful prior leaner, which flexibly...
In this paper we introduce a novel method to simulate lateral diffusion of inclusions in a fluctuating membrane. The regarded systems are governed by two dynamic processes: the height fluctuations of the membrane and the diffusion of the inclusion...
The slow inference process of image diffusion models significantly degrades interactive user experiences. To address this, we introduce Diffusion Preview, a novel paradigm employing rapid, low-step sampling to generate preliminary outputs for user ev...
The evolution of diffusion models has greatly impacted video generation and understanding. Particularly, text-to-video diffusion models (VDMs) have significantly facilitated the customization of input video with target appearance, motion, etc. Despit...
A two stream model of boron diffusion in silicon has been developed. The model is intended for simulation of transient enhanced diffusion including redistribution of ion-implanted boron during low temperature annealing. The following mechanisms of bo...
We study charge diffusion in holographic scaling theories with a particle-hole symmetry. We show that these theories have a universal regime in which the diffusion constant is given by $D_c = C v_B^2/ (2 πT)$ where $v_B$ is the velocity of the butte...
Diffusion models have achieved remarkable success across a range of generative tasks. Recent efforts to enhance diffusion model architectures have reimagined them as a form of multi-task learning, where each task corresponds to a denoising task at a...
Generating safe, kinodynamically feasible, and optimal trajectories for complex robotic systems is a central challenge in robotics. This paper presents Safe Model Predictive Diffusion (Safe MPD), a training-free diffusion planner that unifies a model...
Established theoretical studies of diffusion in rugged (or rough) potential surfaces have largely focused on quenched energy landscapes. Here we study diffusion on a rugged energy landscape in the presence of dynamic disorder, a situation relevant to...
A new sequence for single-voxel diffusion-weighted 1H MRS (DWS), named DW-SPECIAL, is proposed to improve the detection and subsequent estimation of the diffusion properties of strongly J-coupled metabolites. It combines the semi-adiabatic SPECIAL se...
This is a brief "proof of concept" article that shows nonlocal diffusion is well suited to the study of pattern formation and the particular application of public sentiment. We use a nonlocal reaction-diffusion equation to model the evolution of publ...