In the paper Neural Autoregressive Distribution Estimation (Uria et al., 2016), NADE (and other autoregressive models) seem to be described as neither directed or undirected models:
We’ve described the Neural Autoregressive Distribution Estimator, a tractable, flexible and competitive alternative to directed and undirected graphical models for unsupervised distribution estimation
NADE thus substantially differs from this literature focusing on directed and undirected models, benefiting from a few properties that these approaches lack. Mainly, NADE does not rely on latent stochastic hidden units, making it possible to tractably compute its associated data likelihood for some given ordering. This in turn makes it possible to efficiently produce exact samples from the model (unlike in undirected models) and get an unbiased gradient for maximum likelihood training (unlike in directed graphical models).
These slides by Russ Salakhutdinov seem to agree that autoregressive models (subset of fully observed) are separate from "undirected DGMs" and "directed DGMs":
How is this possible? Is it because autoregressive models lack a hierarchy?
However, my intuition is that they are directed, as the Flow-GAN blogpost by Aditya Grover and Manik Dhar suggests.
Similarly, according to a tutorial on generative models by Shakir Mohamed and Danilo Rezende from DeepMind at UAI 2017 (video recording and slides), autoregressive models such as NADE and PixelCNN are classified as directed models: