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A trained diffusion model can be sampled in many ways, with different efficiency and quality. There are various equivalent formalisms, including Markov chains, denoising diffusion probabilistic models, noise conditioned score networks, and stochastic differential equations. [3] They are typically trained using variational inference. [4]
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.
In probability theory and statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion process is stochastic in nature and hence is used to model many real-life stochastic systems.
a generative model is a model of the conditional probability of the observable X, given a target y, symbolically, (=) [2] a discriminative model is a model of the conditional probability of the target Y , given an observation x , symbolically, P ( Y ∣ X = x ) {\displaystyle P(Y\mid X=x)} [ 3 ]
Knudsen diffusion, named after Martin Knudsen, is a means of diffusion that occurs when the scale length of a system is comparable to or smaller than the mean free path of the particles involved. An example of this is in a long pore with a narrow diameter (2–50 nm) because molecules frequently collide with the pore wall. [ 1 ]
The Ehrenfest model (or dog–flea model) of diffusion was proposed by Tatiana and Paul Ehrenfest to explain the second law of thermodynamics. [1] [2] The model considers N particles in two containers. Particles independently change container at a rate λ.
A jump-diffusion model is a form of mixture model, mixing a jump process and a diffusion process. In finance, jump-diffusion models were first introduced by Robert C. Merton. [6] Such models have a range of financial applications from option pricing, to credit risk, to time series forecasting. [7]
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 ...