Generative Models

Generative models learn the probability distribution of their training data, p(x), well enough to produce new samples that look like it — images, audio, text, molecules. Discriminative models learn p(y | x) to label data; generative models learn to create it.

This landing page compares the four major families and links to a deep dive for each.

1. Topics

Autoencoders

Encoder-decoder networks that compress data to a bottleneck code; denoising, sparse, and anomaly-detection uses.

Variational Autoencoders

Probabilistic autoencoders with the reparameterization trick and ELBO; smooth latent spaces for sampling.

GANs

Generator vs discriminator minimax training; DCGAN, StyleGAN, CycleGAN, and how to stabilise training.

Diffusion Models

Learn to reverse a gradual noising process; DDPM, latent diffusion, classifier-free guidance.

Autoregressive (GPT-style)

Factorise p(x) into next-token predictions with Transformers; the basis of modern LLMs.

2. How the Families Compare

Four Families of Deep Generative Models VAE x → z → x̂ encode / decode GAN z → G → D adversarial game Diffusion noise → … → x iterative denoise Autoregressive p(x_t | x_<t) next token Sample quality blurry-ish sharp very sharp very sharp Sampling speed 1 pass 1 pass many steps 1 pass / token Likelihood lower bound none bound exact Training stable unstable stable stable Today: diffusion leads images/audio/video; autoregressive Transformers lead text and code.

Autoencoders and VAEs learn an encoder to a latent space and a decoder back. VAEs make that space probabilistic so you can sample from it. GANs train a generator against a discriminator; samples are sharp but training can be unstable and suffer mode collapse. Diffusion models learn to remove noise step by step; they give high-quality, diverse samples at the cost of many network evaluations per sample (reduced with fewer-step samplers and distillation). Autoregressive models generate one token at a time with exact likelihood; scaled Transformers of this kind are today's LLMs.

The families combine: Stable Diffusion runs diffusion inside a VAE's latent space with a CLIP-style text encoder; image tokenizers (VQ-VAE) let autoregressive Transformers generate images.

3. Milestones

Timeline 2013 VAE 2014 GAN 2015 DCGAN 2017 CycleGAN 2018 GPT / StyleGAN 2020 DDPM 2021 DALL-E, CLIP 2022 Latent Diffusion Note: DCGAN was published late 2015; dates are first-paper years.

Each family took the lead in turn on image synthesis: VAEs and GANs in the 2010s, diffusion from roughly 2021. Evaluation remains hard: FID compares feature statistics of real and generated images, but human preference studies and task-specific checks are still needed.

5. Choosing a Family

As a rule of thumb, use diffusion for high-fidelity images, autoregressive transformers for text and code, GANs where fast single-pass sampling matters, and VAEs when you need a smooth latent space for interpolation or compression.