One Decode, Fifty Denoises

Two systems produce the same $512 \times 512$ image from the same prompt.

Pixel diffusion runs the denoiser directly on the $512 \times 512$ grid, so what comes out of the last step is already the image.
Latent diffusion runs the same denoiser on a $64 \times 64$ latent grid, then decodes that final latent into pixels once.

Both run 50 sampling steps, and both encode the prompt once. Take the denoiser's cost to be proportional to the number of cells in the grid it runs on.

part	when it runs	cost
text encoder	once per image, both systems	$2$
denoiser on the $64 \times 64$ latent	once per sampling step	$1$
denoiser on the $512 \times 512$ pixel grid	once per sampling step	derive it
decoder, latent $\to$ pixels	once per image, latent system only	$20$

Counting every part of each system, how many times cheaper is the latent pipeline than the pixel one? Choose the closest value.

One Decode, Fifty Denoises

Hints