<p>Deep learning has been reshaping traditional manufacturing into intelligent, data-driven processes. Generative models, represented by Generative Adversarial Networks (GANs), offer a powerful paradigm for data generation, addressing critical challenges of data scarcity and imbalance in manufacturing applications. This paper presents a comprehensive tutorial on the principles and applications of GANs, with a focused exploration of their use in intelligent welding. First, the foundational concepts of GANs and their key variants are reviewed, highlighting their adversarial learning mechanisms and architectural differences. The paper then surveys the deployment of GANs across diverse welding tasks, including seam tracking, defect detection and classification, process outcome prediction, and weld-pool synthesis. Finally, a detailed case study demonstrates weld-pool image generation using a β-Total Correlation Variational Autoencoder (β-TC VAE) to model weld pool features in a structured latent space, combined with a PatchGAN to recover high-frequency visual details for realistic synthesis. This tutorial provides a foundation for researchers and practitioners to leverage generative models in welding and other advanced manufacturing fields.</p>