What is the difference between VAE and Normalizing Flow?

[Litou1]

Congrats and excellent work! Maybe a dumb question, what's the difference between this and VAE, and how are they related?

[jayzhan211]

Congrats and excellent work! Maybe a dumb question, what's the difference between this and VAE, and how are they related?

Maybe you can refer to NVAE: A Deep Hierarchical Variational Autoencoder

[andreas128]

Thanks, great question!

What are the architectural differences of VAE and NF?

For autoencoders, the encoder and decoder are two separate networks and usually not invertible. A Normalizing Flow is bijective and applied in one direction for encoding and the other for decoding. That means that you obtain the exact same image after encoding an image into latent space and decoding it again.

What are the training objectives of VAE and NF?

• VAE: Maximize the lower bound of the log-likelihood (ELBO)
• NF: Minimize the exact negative log-likelihood