The mathematical basics of diffusion

Diffusion models have many interacting parts. Building machine learning models requires a holistic understanding of how all these parts interact: the theory for an idealized setting; numerical errors and approximations; and other hidden knowledge.

Luckily however, diffusion models are also somewhat unique in machine learning in having a well motivated and deep theory which can be used to make predictions for how they behave in practice. Having theoretically-based intuition can take us a long way.

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