Noise in Diffusion Models Is a Learnable Input

Model training consumes concrete random inputs that enter the realized loss and optimization. Because training aims to reduce this loss, models can learn to exploit accessible structure in these inputs, making realized randomness itself learnable content. We establish this learning mechanism in diffusion models, where clean data and target noise jointly form the noisy input. Prediction gains can arise from clean-data regularities, noise structure, and their interaction, so lower loss need not indicate better learning of clean-data regularities. We test this mechanism with controlled, reproducible pseudorandom number generator (PRNG) streams on MNIST and CIFAR-10. Random-role ablations localize the dominant effect to diffusion noise. Without reusable clean-image structure, structured-noise training can lower loss below the IID reference, while IID testing reverses this advantage, demonstrating learned noise dependence. Value-preserving shuffling largely removes these gains, identifying ordering as a major source of learnable structure. Matched-source initialization improves representative generations, supporting learned noise as a generation cue. Prior results on noise–data assignment, noise-based backdoors, and structured video noise provide independent evidence of learned use of noise structure and noise–data relationships, including in large generative models. These studies also demonstrate that noise design can exploit this learnability to achieve specific goals or improve model performance. These findings motivate testing whether existing large generative models learn structure in industrial-grade PRNG outputs that affects generation quality. Our view establishes noise as a learnable and therefore designable input dimension for guiding learning and generation.