HJB Tutorial Bridges RL, Diffusion Models

This is the rare theory-heavy AI tutorial that earns its length: it gives one clean control-theoretic frame for continuous-time RL and diffusion models, which makes both topics feel like different views of the same math.

• –The LQR and Merton examples are the right validation cases because they have closed-form optima and let the neural policy-iteration setup prove itself.
• –The diffusion section is the most interesting part: reverse-time sampling becomes a finite-horizon control problem, and the score function emerges as the optimal drift correction.
• –The post assumes comfort with SDEs, PDEs, and convex duality, so it is more of an advanced bridge piece than a beginner-friendly walkthrough.
• –HN traction suggests there is still a hungry audience for rigorous AI math when it pays off with a unifying story.