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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]
Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios. Therefore, diffusion and the corresponding mathematical models are used in several fields beyond physics, such as statistics , probability theory , information theory , neural networks , finance ...
The technology adoption lifecycle is a sociological model that is an extension of an earlier model called the diffusion process, which was originally published in 1956 by George M. Beal and Joe M. Bohlen. [1]
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.
The diffusion of an innovation typically follows an S-shaped curve which often resembles a logistic function. Roger's diffusion model concludes that the popularity of a new product will grow with time to a saturation level and then decline, but it cannot predict how much time it will take and what the saturation level will be.
Crossing the Chasm is an adaptation of an innovation-adoption model called diffusion of innovations theory created by Everett Rogers, The author argues there is a chasm between the early adopters of the product (the technology enthusiasts and visionaries) and the early majority (the pragmatists).
Reaction–diffusion systems are mathematical models that correspond to several physical phenomena. The most common is the change in space and time of the concentration of one or more chemical substances: local chemical reactions in which the substances are transformed into each other, and diffusion which causes the substances to spread out ...
The Bass diffusion model is derived by assuming that the hazard rate for the uptake of a product or service may be defined as: = () = + [()] where () is the probability density function and () = is the survival function, with () being the cumulative distribution function.