Generative Models

This chapter explores four types of generative models – energy-based models (EBMs), variational autoencoders (VAEs), generative adversarial networks (GANs) and latent diffusion models (LDMs) – focusing primarily on image generation. The chapter begins by introducing the central idea of generative models: training a model to produce samples from the same distribution as the training data, transforming random variables from a source distribution (e.g., uniform or normal) into realistic outputs. EBMs, which rely on Markov chain Monte Carlo (MCMC) techniques, are discussed first, followed by VAEs, which extend autoencoders. GANs, the most developed generative models, are examined in depth, including their variants like StyleGAN, WGAN, and SNGAN. The chapter also covers LDMs, representing the current state-of-the-art in image generation. Key datasets used include MNIST and CIFAR10, with performance evaluated using metrics like the inception score and Fréchet inception distance. The chapter concludes by discussing the broader applications of generative models, including their potential in quantitative finance, and provides a framework for comparing and evaluating these models.