Prerequisites & Notation

This chapter requires nn.Module and CNNs (Chapters 26-27). Familiarity with probability distributions (Chapter 9) is helpful.

nn.Module, training loops, CNNs (Chapters 26-27)(Review ch27)
Self-check: Can you build a U-Net and train it?
Probability distributions and sampling (Chapter 9)(Review ch09)
Self-check: Can you sample from a Gaussian and compute KL divergence?

Symbol	Meaning	Introduced
$p_{\\theta}(\\mathbf{x})$	Model distribution parameterised by $\theta$	s01
$q_{\\phi}(\\mathbf{z}\|\\mathbf{x})$	Encoder (approximate posterior) in VAE	s01
$D_{\\text{KL}}$	Kullback-Leibler divergence	s01
$\\varepsilon_t$	Noise added at diffusion step $t$	s03
$\\beta_t$	Noise schedule coefficient	s03