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Pseudorandom Streams within Diffusion Models Act as Learnable Inputs That Affect Generation Quality

Digital learning systems consume concrete pseudorandom values rather than abstract random variables. These values enter the realized loss and its gradient during training. If a pseudorandom stream contains structure that is accessible to the model, this structure can therefore become part of what the learning system learns. We show that this effect can be strong enough to change generation quality in diffusion models. For diffusion noise prediction, there are two related routes by which the loss can be reduced. The model can learn regularities of the clean data and use them to infer the added noise. It can also exploit regularities of the noise source itself to recover the realized noise from the noisy input. Random-role ablation shows that the dominant source-dependent effect in our experiments is associated with the diffusion-noise roles. A diffusion probe that removes reusable real-image structure still shows clear source-dependent noise-prediction learning, and its source ordering closely matches that of real-data diffusion training. Different pseudorandom sources also produce large differences in generation quality on MNIST and CIFAR-10. Further experiments show that the same source structure can also be learned in an independent next-value prediction task, although this is not the learning mechanism used by the diffusion model. Changing the probe clean reference preserves much of the source ordering while changing the numerical response, producing clean-reference-dependent power-law relations. Overall, the results show that a pseudorandom stream is not only a source of stochastic variation: its concrete structure can act as a learnable input whose effect depends on the learning system.

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