Generative AI

4.

Core Generative Model Architectures

4.1.

Autoregressive Models

4.1.1.

Sequential Generation

4.1.1.1.

Next-Token Prediction

4.1.1.2.

Conditional Independence Assumptions

4.1.2.

Language Models

4.1.2.1.

4.1.2.2.

Neural Language Models

4.1.2.3.

Transformer Language Models

4.1.3.

Autoregressive Image Models

4.1.3.1.

4.1.3.2.

4.1.3.3.

4.2.

Variational Autoencoders

4.2.1.

Encoder-Decoder Framework

4.2.1.1.

Encoder Architecture

4.2.1.2.

Decoder Architecture

4.2.1.3.

Latent Space Representation

4.2.2.

Variational Inference

4.2.2.1.

Evidence Lower Bound

4.2.2.2.

Reparameterization Trick

4.2.2.3.

Posterior Approximation

4.2.3.

Loss Function Components

4.2.3.1.

Reconstruction Loss

4.2.3.2.

KL Divergence Regularization

4.2.3.3.

Beta-VAE Variants

4.2.4.

Applications and Extensions

4.2.4.1.

Conditional VAEs

4.2.4.2.

Hierarchical VAEs

4.2.4.3.

Disentangled Representations

4.3.

Generative Adversarial Networks

4.3.1.

Adversarial Framework

4.3.1.1.

Generator Network

4.3.1.2.

Discriminator Network

4.3.1.3.

Minimax Game Theory

4.3.2.

Training Dynamics

4.3.2.1.

Nash Equilibrium

4.3.2.2.

4.3.2.3.

Training Instability

4.3.3.

4.3.3.1.

Deep Convolutional GANs

4.3.3.2.

Conditional GANs

4.3.3.3.

Wasserstein GANs

4.3.3.4.

Progressive GANs

4.3.3.5.

StyleGAN Family

4.3.3.6.

4.3.4.

Evaluation Metrics

4.3.4.1.

Inception Score

4.3.4.2.

Fréchet Inception Distance

4.3.4.3.

Precision and Recall

4.4.

Diffusion Models

4.4.1.

Forward Diffusion Process

4.4.1.1.

Noise Scheduling

4.4.1.2.

Markov Chain Formulation

4.4.2.

Reverse Diffusion Process

4.4.2.1.

Denoising Networks

4.4.2.2.

Score-Based Models

4.4.3.

Training Objectives

4.4.3.1.

Denoising Score Matching

4.4.3.2.

Variational Lower Bound

4.4.4.

Sampling Methods

4.4.4.1.

4.4.4.2.

4.4.4.3.

Accelerated Sampling

4.4.5.

Conditional Generation

4.4.5.1.

Classifier Guidance

4.4.5.2.

Classifier-Free Guidance

4.5.

Flow-Based Models

4.5.1.

Normalizing Flows

4.5.1.1.

Invertible Transformations

4.5.1.2.

Change of Variables Formula

4.5.2.

Coupling Layers

4.5.2.1.

Affine Coupling

4.5.2.2.

Neural Spline Flows

4.5.3.

Autoregressive Flows

4.5.3.1.

Masked Autoregressive Flows

4.5.3.2.

Inverse Autoregressive Flows

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5. Transformer Architecture and Language Models