Pseudorandom Number Streams Are a Learnable Input to Diffusion Models, Measurably Changing Generation Quality

arXiv 2608.02575·low signalXBlueskyLinkedInCopy link

Diffusion models consume 'randomness' that on finite-precision hardware is a deterministic numerical orbit, and this paper shows that orbit structure becomes a learnable input affecting both training and generation. A small MLP predicting the next orbit value measures general sequence predictability, while a diffusion probe replacing real images with online random tensors measures whether the model can exploit orbit structure. After controlling marginal statistics and screening out dynamical and finite-precision failures, surviving orbits still produce markedly different diffusion losses and generation quality on MNIST and CIFAR-10, with probe loss and real-data diffusion loss approximately following a power law after IID normalization.