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In the area of probability and stochastic processes, stochastic flows, which are defined as special random transformations, are mostly determined by stochastic differential equations. A very important topic in stochastic differential equations is diffusion equations. The focus of this talk will be the weak solutions of some diffusion equations and new stochastic flows defined through them. Correlated Brownian motion equation, one-sided and two-sided sticky equations, and diffusions with rank-based coefficients will be overviewed.