VAEs and Flows

VAEs and normalizing flows are likelihood-oriented generative models. They are useful for understanding latent variables, amortized inference, variational bounds, vector quantization, exact likelihoods, and invertible transformations.

Variational Autoencoders and Discrete Latents

Year	Paper	Topic	Note
2013	Auto-Encoding Variational Bayes	VAE	Reparameterization trick and amortized variational inference.
2015	Importance Weighted Autoencoders	IWAE	Tighter variational bound using importance-weighted samples.
2016	beta-VAE	Disentanglement	Adjusts the KL weight to encourage factorized latent structure.
2017	Neural Discrete Representation Learning	VQ-VAE	Discrete latent codes learned with vector quantization.
2019	Generating Diverse High-Fidelity Images with VQ-VAE-2	VQ-VAE-2	Hierarchical discrete latents for high-quality image synthesis.
2020	Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images	VDVAE	Very deep hierarchical VAE with strong likelihood performance.
2020	NVAE	Deep VAE	Scalable normalizing-flow-enhanced VAE architecture.

Normalizing Flows

Year	Paper	Topic	Note
2014	NICE: Non-linear Independent Components Estimation	Coupling flows	Early tractable invertible density model.
2015	Variational Inference with Normalizing Flows	Normalizing flows	Flexible posteriors via invertible transformations.
2016	Improving Variational Inference with Inverse Autoregressive Flow	IAF	Autoregressive flow for richer approximate posteriors.
2016	Density Estimation Using Real NVP	Real NVP	Coupling layers with exact likelihood and sampling.
2017	Masked Autoregressive Flow for Density Estimation	MAF	Autoregressive density estimator as a flow.
2018	Glow (code)	Flow	Invertible 1x1 convolutions for scalable image flows.
2018	FFJORD	Continuous normalizing flow	Unbiased trace estimator for scalable continuous-time flows.
2019	Neural Spline Flows	Spline flows	Monotonic rational-quadratic splines for flexible invertible transforms.

Reading Path

Step	Read
1	Auto-Encoding Variational Bayes and IWAE.
2	VQ-VAE and VQ-VAE-2 for discrete latent tokenization.
3	NICE, Real NVP, Glow, and Neural Spline Flows for exact-likelihood flows.
4	FFJORD before moving to Flow Matching and Fast Sampling.