This episode provides a comprehensive monograph on diffusion models, detailing their foundational principles through three unifying perspectives: the Variational View (related to VAEs and DDPMs), the Score-Based View (rooted in EBMs and Score SDEs), and the Flow-Based View (connecting to Normalizing Flows and Flow Matching). The core concept involves defining a continuous forward process that adds noise and then learning a corresponding reverse process—a Stochastic Differential Equation (SDE) or Probability Flow Ordinary Differential Equation (PF-ODE)—to transform noise back into data. Much of the discussion focuses on the mathematical equivalence of these different formulations, the tractable training objectives (like Denoising Score Matching), and advanced techniques for accelerating the slow sampling process, including sophisticated numerical ODE solvers (like DPM-Solver) and distillation methods (such as Consistency Models). Finally, the monograph explores the theoretical connection between diffusion models and Optimal Transport (OT), suggesting that diffusion is related to, but not generally equivalent to, solving the optimal transport problem.

Reference:

Lai, C. H., Song, Y., Kim, D., Mitsufuji, Y., & Ermon, S. (2025). The Principles of Diffusion Models. arXiv preprint arXiv:2510.21890.