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Unification: SDEs, Probability Flow ODEs, and Fokker-Planck Dynamics

Chapter 21 · Mathematics for AI and Machine Learning · Advanced · 1:34

An interactive live film: microscopic random SDE paths and smooth deterministic ODE streamlines are united by the macroscopic Fokker-Planck probability current, yielding identical density marginals at every moment.

Narration

We have seen three different languages for diffusion models: stochastic differential equations, probability flow ordinary differential equations, and the Fokker-Planck equation.

At the macroscopic level, the Fokker-Planck equation describes the conservation of probability mass. The rate of change of density equals minus the divergence of current.

The rest of the narration is in the book's Companion.

More from Chapter 21

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