To build sophisticated generative models like StyleGAN or Diffusion Models, a solid grasp of the underlying principles is necessary. This chapter revisits the foundational concepts required before we proceed to more advanced techniques.

We will start by reviewing probabilistic modeling for generation, focusing on how models aim to capture data distributions, often denoted as $p_{data}(x)$. We'll categorize the main families of generative models to understand where GANs and Diffusion Models fit.

Next, we address the common difficulties encountered when generating high-dimensional data, such as images or audio, including managing complexity and ensuring diverse outputs. We will then refresh key concepts of Generative Adversarial Networks (GANs), recalling the core components like the generator $G$ and discriminator $D$, and their adversarial training objective, often formulated as a min-max game: $\min_G \max_D V(D, G) = \mathbb{E}_{x \sim p_{data}(x)}[\log D(x)] + \mathbb{E}_{z \sim p_z(z)}[\log(1 - D(G(z)))]$ Finally, we introduce the intuition behind diffusion models, covering the basic ideas of the forward (noising) and reverse (denoising) processes.

Completing this chapter ensures you have the necessary background refreshed to tackle the advanced architectures, training methods, and evaluation techniques presented subsequently.