The Little Book of Generative AI Foundations: An Intuitive Mathematical Primer

arXiv:2605.29713 · cs.LG, cs.AI · Submitted 2026-05-28 · Read on arXiv

cs.LG, cs.AI

Submitted: 2026-05-28

Updated: 2026-09-08

Comments: Revised preprint version, 195 pages. Added visual explanations throughout. Comments and corrections are welcome

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Diffusion Model — 64× in this paper · explained in 8 episodes
• Generative Model — 62× in this paper · explained in 2 episodes
• Diffusion Models — 54× in this paper · explained in 6 episodes
• Generative Models — 34× in this paper · explained in 2 episodes
• Langevin Dynamics — 27× in this paper · explained in 2 episodes
• Latent Space — 18× in this paper · explained in 7 episodes
• Score Function — 15× in this paper · explained in 4 episodes
• Latent Representation — 13× in this paper · explained in 2 episodes
• Trace — 13× in this paper · explained in 2 episodes
• Principal Component Analysis — 12× in this paper
• Wasserstein Distance — 11× in this paper · explained in 4 episodes
• Core — 10× in this paper · explained in 2 episodes
• Generative AI — 10× in this paper · explained in 2 episodes
• Denoising Diffusion Probabilistic Model — 8× in this paper
• Reconstruction Error — 7× in this paper · explained in 2 episodes
• Latent Representations — 6× in this paper · explained in 3 episodes
• Ornstein–Uhlenbeck Process — 5× in this paper · explained in 3 episodes
• Alignment — 4× in this paper · explained in 1 episode
• Singular Value Decomposition — 4× in this paper
• Variational Autoencoder (VAE) — 4× in this paper · explained in 3 episodes
• Adversarial Training — 3× in this paper · explained in 1 episode
• Alternation — 3× in this paper · explained in 1 episode
• Generative Modeling — 3× in this paper · explained in 3 episodes
• Stochastic Dynamics — 3× in this paper · explained in 2 episodes
• Structural Constraints — 3× in this paper · explained in 2 episodes
• Activation Function — 2× in this paper · explained in 1 episode
• Consistency — 2× in this paper · explained in 3 episodes
• Cosine Similarity — 2× in this paper · explained in 3 episodes
• Flow Matching — 2× in this paper · explained in 7 episodes
• Generative Adversarial Networks (GANs) — 2× in this paper · explained in 3 episodes
• Mode Collapse — 2× in this paper · explained in 2 episodes
• Normalizing Flow — 2× in this paper · explained in 3 episodes
• Normalizing Flows — 2× in this paper · explained in 4 episodes
• Principal Component Analysis (PCA) — 2× in this paper · explained in 4 episodes
• Probabilistic Principal Component Analysis — 2× in this paper
• Rectified Flow — 2× in this paper · explained in 3 episodes
• Representation Learning — 2× in this paper · explained in 2 episodes
• Singular Value Decomposition (SVD) — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Adaptation — 1× in this paper · explained in 1 episode
• Decode — 1× in this paper · explained in 2 episodes
• Diffusion Processes — 1× in this paper · explained in 2 episodes
• Distribution Matching — 1× in this paper · explained in 2 episodes
• Expectation Maximisation — 1× in this paper
• Objective Function — 1× in this paper · explained in 2 episodes
• Optimal Transport — 1× in this paper · explained in 5 episodes
• Variational Bayes — 1× in this paper · explained in 2 episodes

Sources

• From Classical Probabilistic Latent Variable Models to Modern Generative AI: A Unified Perspective
• WaveNet: A Generative Model for Raw Audio

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