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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]
It is used heavily in statistical physics, statistical analysis, information theory, data science, neural networks, finance and marketing. A sample path of a diffusion process models the trajectory of a particle embedded in a flowing fluid and subjected to random displacements due to collisions with other particles, which is called Brownian motion.
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.
Library and Information Science Research. 6 (4): 425– 38. 1984. "Information, Mass Media Use, and the Working Poor". Library and Information Science Research. 7 (2): 97– 113. 1985. Chatman, Elfreda A. (1986). "Diffusion Theory: A review and test of a conceptual model in information diffusion". Journal of the American Society for Information ...
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.
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 ...
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 ...
Stable Diffusion is a deep learning, text-to-image model released in 2022 based on diffusion techniques. The generative artificial intelligence technology is the premier product of Stability AI and is considered to be a part of the ongoing artificial intelligence boom.