This monograph develops a concise geometric framework for forward and reverse diffusion processes governed by stochastic differential equations. Beginning from the Fokker–Planck equation and the score function, it constructs the reverse-time SDE of Anderson (1982) and interprets both forward and reverse dynamics as complementary flows acting on probability mass: forward diffusion disperses structure; reverse diffusion reconstructs it.
The exposition assumes familiarity with stochastic calculus and focuses on mathematical structure rather than implementation. A concluding chapter illustrates the framework through the lens of market microstructure, treating the liquidity field as a stochastic object whose latent geometry is revealed by reverse-time dynamics.
Intended as a compact reference for researchers and practitioners working at the intersection of stochastic analysis, geometric probability, and quantitative finance.
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