Can anyone guide me on Degrees of Freedom in VAEs vs. Normalizing Flows?

Hi everyone,

I am currently diving deep into the world of machine learning and have been particularly intrigued by generative models. Recently; I have been exploring Variational Autoencoders (VAEs) and Normalizing Flows, and I am fascinated by how they handle the concept of degrees of freedom.

From what I have gathered, VAEs have a more straightforward structure where the encoder and decoder are neural networks that map the data to and from a latent space. The latent space's dimensionality seems to play a crucial role in determining the model's capacity to generate diverse outputs. However, I am curious about the limitations this structure imposes in terms of flexibility and expressiveness.

On the other hand, Normalizing Flows appear to offer more flexibility by using a series of invertible transformations. This seems to allow them to model more complex distributions without the same restrictions on the latent space's dimensionality. But I wonder how this added flexibility impacts other aspects, such as computational efficiency and model interpretability.

How do the degrees of freedom in VAEs compare to those in Normalizing Flows in practical applications?
Are there specific scenarios where one approach significantly outperforms the other?
What are the trade-offs between using a more structured model like a VAE versus a more flexible model like a Normalizing Flow?

Also, I have gone through this post; which definitely helped me out a lot.

Any real world examples, research papers, or personal experiences would be incredibly helpful. I am looking forward to learning from this knowledgeable community and engaging in a fruitful discussion.

Thanks in advance for your input!

knowledgeable community? man, I hope you find better way do this.
machine learning is beta ideal in the world, no really clear knew what we will got from it.

you can focus VAEs or Normalizing Flows, after done you jobs compare both, the details will show you different.