Ornstein-Uhlenbeck (OU) Heat Flow
Chapter 21: Fokker-Planck and Distribution Dynamics — Ornstein-Uhlenbeck & Heat Equation Solutions
From the book
Chapter 21: Fokker-Planck and Distribution Dynamics. In the chapter mind map this icon labels **Ornstein-Uhlenbeck & Heat Equation Solutions. The discussion below is excerpted and lightly edited from § Ornstein-Uhlenbeck & Heat Equation Solutions** in Mathematics for AI and Machine Learning.
For pure diffusion (no drift, $\mathbf{f} = \mathbf{0}$), the Fokker-Planck equation becomes the heat equation:
This is exactly what happens in the forward diffusion process of diffusion models.
What this drawing shows
What you see. Red initial peak fixed; blue density relaxes toward the mean and widens under OU / heat diffusion.
In the mind map. Chapter 21 — Ornstein-Uhlenbeck & Heat Equation Solutions. See From the book above for definitions, figures, and worked examples.
Where to read next
Read the full definitions, figures, and worked examples in Chapter 21: Fokker-Planck and Distribution Dynamics — see the mind-map node Ornstein-Uhlenbeck & Heat Equation Solutions.
