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We present an accessible first course on the mathematics of diffusion models and flow matching for machine learning. We aim to teach diffusion as simply as possible, with minimal mathematical and machine learning prerequisites, but enough technical detail to reason about its correctness. Unlike most tutorials on this subject, we take neither a Variational Auto Encoder (VAE) nor a Stochastic Differential Equations (SDE) approach. In fact, for the core ideas we will not need any SDEs, Evidence-Based-Lower-Bounds (ELBOs), Langevin dynamics, or even the notion of a score. The reader need only be…
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