The motivation and mechanism of conditional flow

[bearinsuke]

Hi,

Thanks for your incredible contribution! I have a question about understanding the term conditional in your work.
You concatenate the conditional vector in the input of coupling layers since it provides conditional prior. Can I understand it this way: You use conditional vector since your input of the flow part is the output of a pooling layer of a pre-trained CNN, which is impossible to do inverse without using conditional vector. In other words, the conditional vector (your PE) maintains pre-trained CNN's invertibility or makes the inverse more accurate.
If I understand it right, could you please provide some mathematical evidence or some supplementary content to prove this point? If not, how can I understand the conditional vector and positional prior and how does it work?
Thanks for your time.

Best regards