Chapter 21: Fokker-Planck and Distribution Dynamics. In the chapter mind map this icon labels Fokker-Planck Equation: Drift & Diffusion Terms. The discussion below is excerpted and lightly edited from § Simplifying the Langevin Fokker-Planck Equation in Mathematics for AI and Machine Learning.

Using the identity $\nabla \cdot (p_t \nabla \log p) = \nabla \cdot \left(p_t \frac{\nabla p}{p}\right) = \nabla \cdot \nabla p = \nabla^2 p$, the equation simplifies to:

This shows that the distribution $p_t$ evolves toward the target distribution $p$. When $p_t = p$, we have $\frac{\partial p_t}{\partial t} = 0$, confirming that $p$ is a stationary solution.