Understanding Weiner Process

Motivation

I wrote this blog as I was trying to understand the math behind the diffusion model.Though one can understand the algorithm of differernt types of formulation under diffusion models such as herirachical VAE, Score based models, Rectiflow, flow models without knowing much about SDE, to understand in detail why they all fall under the same category I beleive a deeper understanding of weineer process, OU process is needed, especaily the stochastic calculas which is the key to ITO’s lemma, forward and backward equations.
In this section a brief informal intro to wiener process and why stocastic calculas is provided and in the later section a formal definition is tried to be given.

To read more click the link below. Since writing math using plain html is time consuming, I use jupyter-book for wrtiing my blogs. (To read comfortably please toggle the side bar)

https://yogheswaran-a.github.io/blogs/01_weiner_process.html