The "input image" is just the noisy sample from the previous timestep, yes.
The overall architecture diagram does not explicitly show the conditioning mechanism, which is a small separate network. For this paper, we only trained on class-conditional ImageNet and completely unconditional megapixel-scale FFHQ.
Training large-scale text-to-image models with this architecture is something we have not yet attempted, although there's no indication that this shouldn't work with a few tweaks.
