The Path from PCA to Autoencoders to Variational Autoencoders: Building Intuition for Deep Generative Modeling Tharwat, Alaa Eid, Mahmoud M. This tutorial provides a comprehensive and intuitive journey through the evolution of deep generative models, tracing a clear path from the foundations of Principal Component Analysis (PCA) to modern Variational Autoencoders (VAEs), showing how each method solves the limitations of the previous one. We begin with PCA, a linear tool for reducing data dimensions. Its inability to model non-linear patterns motivates the use of Autoencoders (AEs), which use neural networks to learn flexible, compressed representations. However, AEs lack a probabilistic framework, preventing them from generating new data. VAEs address this by treating the latent space as a probability distribution, enabling data generation. We compare the three methods through theoretical analysis, experiments, and step-by-step numerical examples that show exactly how each model compresses data—a detail often missing elsewhere. Unlike resources that treat these topics separately, we connect them into a single narrative, building intuition progressively from linear to probabilistic deep generative models. MDPI AG 2026 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_6501 https://www.hsbi.de/publikationsserver/record/7141 Tharwat A, Eid MM. The Path from PCA to Autoencoders to Variational Autoencoders: Building Intuition for Deep Generative Modeling. <i>Stats</i>. 2026;9(2). doi:<a href="https://doi.org/10.3390/stats9020023">10.3390/stats9020023</a> eng info:eu-repo/semantics/altIdentifier/doi/10.3390/stats9020023 info:eu-repo/semantics/altIdentifier/issn/2571-905X info:eu-repo/semantics/openAccess