CENTRAL INSIGHT The Langevin perspective reveals a fundamental triangular relationship.

Forward Process Reverse Process Langevin Dynamics (Identity)

\( p_t(\mathbf{x}) \)

\( p_t(\mathbf{x}) \)

\( p_{t+\Delta t}(\mathbf{x}) \)

This illustrates that the forward and reverse diffusion steps are simply a SPLIT of a single step of Langevin dynamics.

Langevin dynamics is an IDENTITY map on distributions, the forward and reverse diffusion steps are INVERSES of each other at the distribution level.