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In the paper [6] Nadler et al. showed how to design a kernel that reproduces the diffusion induced by a Fokker–Planck equation. They also explained that, when the data approximate a manifold, one can recover the geometry of this manifold by computing an approximation of the Laplace–Beltrami operator. This computation is completely ...
The goal of diffusion models is to learn a diffusion process for a given dataset, such that the process can generate new elements that are distributed similarly as the original dataset. A diffusion model models data as generated by a diffusion process, whereby a new datum performs a random walk with drift through the space of all possible data. [2]
The Latent Diffusion Model (LDM) [1] is a diffusion model architecture developed by the CompVis (Computer Vision & Learning) [2] group at LMU Munich. [ 3 ] Introduced in 2015, diffusion models (DMs) are trained with the objective of removing successive applications of noise (commonly Gaussian ) on training images.
Diffusion-limited aggregation (DLA) is the process whereby particles undergoing a random walk due to Brownian motion cluster together to form aggregates of such particles. This theory, proposed by T.A. Witten Jr. and L.M. Sander in 1981, [ 1 ] is applicable to aggregation in any system where diffusion is the primary means of transport in the ...
Diagram of the latent diffusion architecture used by Stable Diffusion The denoising process used by Stable Diffusion. The model generates images by iteratively denoising random noise until a configured number of steps have been reached, guided by the CLIP text encoder pretrained on concepts along with the attention mechanism, resulting in the desired image depicting a representation of the ...
Confusion inevitably involves some diffusion, [6] so a design with a very wide-input S-box can provide the necessary diffusion properties, [citation needed] but will be very costly in implementation. Therefore, the practical ciphers utilize relatively small S-boxes, operating on small groups of bits ("bundles" [ 7 ] ).
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In numerical linear algebra, the alternating-direction implicit (ADI) method is an iterative method used to solve Sylvester matrix equations.It is a popular method for solving the large matrix equations that arise in systems theory and control, [1] and can be formulated to construct solutions in a memory-efficient, factored form.