In this paper, we investigate the computational complexity of solutions to the Laplace and the diffusion equation. We show that for a certain class of initial-boundary value problems of the Laplace and the diffusion equation, the solution operator is...
Diffusion models that are based on iterative denoising have been recently proposed and leveraged in various generation tasks like image generation. Whereas, as a way inherently built for continuous data, existing diffusion models still have some limi...
Preface to the special issue "Characterisation of Physical Processes from Anomalous Diffusion Data" associated with the Anomalous Diffusion Challenge ( https://andi-challenge.org ) and published in Journal of Physics A: Mathematical and Theoretical....
Latent Couple extension (two shot diffusion port) (⭐ 735)
Create ? videos with Stable Diffusion by exploring the latent space and morphing between text prompts (⭐ 4666)
The concept of cross diffusion is applied to some biological systems. The conditions for persistence and Turing instability in the presence of cross diffusion are derived. Many examples including: predator-prey, epidemics (with and without delay),...
The diffusion of innovations theory has been studied for years. Previous research efforts mainly focus on key elements, adopter categories, and the process of innovation diffusion. However, most of them only consider single innovations. With the deve...
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...
A collection of resources on controllable generation with text-to-image diffusion models. (⭐ 1112)
Papers and resources on Controllable Generation using Diffusion Models, including ControlNet, DreamBooth, IP-Adapter. (⭐ 503)
A latent text-to-image diffusion model (⭐ 72634)
Stable Diffusion web UI (⭐ 161534)
High-Resolution Image Synthesis with Latent Diffusion Models (⭐ 13877)
Runway Inpainting based on Stable Diffusion (⭐ 27)
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...