After adding noise to a training sample, there's still some information about the original contained in the noisy image, so the model only needs to fix it up a

After adding noise to a training sample, there's still some information about the original contained in the noisy image, so the model only needs to fix it up a little with the help of the prompt. But when you start from 100% noise, all of the information needs to come from the model and the prompt. Seen from another angle, if you take a random value for each pixel, you're unlikely to generate anything resembling a picture, let alone any given training picture you're trying to reproduce. That there's an input that makes the model output a training sample doesn't necessarily mean that it's easy to find. But the paper shows that you can find several by guessing randomly.