So there's almost a kilobyte of missing data, without which nothing is produced.

Would a JPEG file with random noise in it be potentially any given original image? Of course not - even though the decompressor is perfectly capable of recreating one given suitable input data.

The "Grokking Stable Diffusion" colab posted here a week or two back makes this particularly explicit - any given 512x512 image can be reversed into a latent-space encoding of that image, and reconstructed from it. The NN weights are necessary but not sufficient to do so - ultimately you end up with a 512 byte number mapping to the expression which reconstructs an image. But that includes images which aren't part of the original training set.

[1] https://colab.research.google.com/drive/1dlgggNa5Mz8sEAGU0wF...