In diffusion model, the data point x_0 is gradually transformed into Gaussian noise. This process is described by a forward stochastic differential equation (SDE) defined on an interval starting at t=0 and ending at t= T
dx_t = f(x_t,t)dt + g(t) dw_t ,where f is called the drift term and g is called the diffusion term, respectively. For mathematical convenince, f is set to be a affine transformation of the state x_t and g is a real-valued function of t .