How to derive the Equation 1?

[AaronHeee]

Sorry I have to re-open an issue as the same as #20, where I posted my attempt to derive the equation 1 but cannot get the result. Could you let me know what I miss? Thanks!

[geweihgg]

Hi，I've tried to derive the equation 1, and get the same result as yours in https://github.com/openai/DALL-E/issues/20. Have you figured it out? Looking forward to your reply, thanks very much!

[YUYUEinFDU]

i have tried to derive the equation (1) using KL divergence between q(z|x) and p(z|x,y), which also does not work. hope the authors could give a clear and complete derive

[finbarrtimbers]

Hey folks- I was also confused by this, so I wrote up the derivation. I'd appreciate a second check over my math.

[ahmdtaha]

I have been looking into this equation for sometime. I wrote my thoughts in the attached main.pdf. I believe we need to convert a single-variable distribution $q_{\phi}(z|x)$ into a multi-variable distribution $q_{\phi}(y,z|x)$ to derive this equation. Yet, I am not sure if I made the right assumptions. I hope someone look into my derivation and share some feedback.