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The Generative AI Wiki

A reference on generative models for students of AI and ML: the math, the models, and how they are used in practice. 50 articles, each with intuition, derivations, worked examples and code.

New here? Start with What is generative AI?, or follow the study roadmap.

The field at a glance

graph TD
    A["Generative modelling<br/>learn p(x) or p(x|c), then sample"] --> B[Explicit density]
    A --> C[Implicit density]

    B --> D["Tractable<br/>exact likelihood"]
    B --> E["Approximate<br/>bound the likelihood"]

    D --> D1["Autoregressive<br/>PixelCNN, WaveNet, GPT"]
    D --> D2["Normalizing flows<br/>RealNVP, Glow"]

    E --> E1["VAE<br/>variational bound"]
    E --> E2["Diffusion<br/>denoising ELBO"]
    E --> E3["Energy-based<br/>contrastive divergence"]

    C --> C1["GAN<br/>adversarial game"]
    C --> C2["Flow matching<br/>simulation-free ODE"]

    D1 --> F["Modern LLMs"]
    E2 --> G["Modern image/video/audio"]
    C2 --> G

    style A fill:#2d3748,stroke:#4a5568,color:#fff
    style F fill:#2b6cb0,stroke:#2c5282,color:#fff
    style G fill:#276749,stroke:#22543d,color:#fff

Every generative model learns something close to the data distribution and samples from it. The families differ in how they handle the likelihood. See the taxonomy for the full comparison.

Foundations

Classical generative models

Sequence models

Large language models

Diffusion and vision

Applications

Evaluation, safety and ethics

Reference

About this wiki

  • Every page starts with a summary and its prerequisites, and ends with key takeaways and further reading.
  • Callout boxes mark intuition (the mental model) and pitfalls (mistakes people actually make).
  • Numbers that date quickly (model sizes, benchmark scores, prices) were last checked in September 2026. The math does not go out of date.
  • To run the site locally: pip install -r requirements.txt, then make serve.