Comment by gwern

This apparently doesn't apply here, but in fact, pixels can be generated independently of each other. There are architectures where you can generate an arbitrary pixel or element of the image without generating the others; they are just implicit. See NeRFs or 'single-pixel GANs' or MAEs: eg https://arxiv.org/abs/2003.08934 https://arxiv.org/abs/2011.13775 https://arxiv.org/abs/2401.14391

Why is this possible? I tend to think of it as reflecting the ability to 'memorize' all possible data, and the independent generation is just when you 'remember' a specific part of a memory. The latent space is a Platonic object which doesn't change, so why should your generative process for materializing any specific point in the latent space have to? It's not surprising if you could generate arbitrary points from a function like 'y = mx + b' without generating every other point, right? It's just an atemporal mathematical object. Similarly with 'generating images from a random seed'. They too are just (complicated) functions mapping one number to another number.

(You might wonder if this is limited to images? It is not. In fact, you can generate even natural language like this to some degree: https://github.com/ethan-w-roland/AUNN based on my proposal for taking the 'independent generation' idea to a pathological extreme: https://gwern.net/aunn )