Diffusion models trained on entirely separate slices of a dataset keep generating nearly identical images — and now there is a mathematical explanation for why.
A team of researchers applied random matrix theory (RMT) — a branch of math that describes the statistical behavior of large matrices — to the linear mechanics inside diffusion models. Their finding: the shared Gaussian statistics baked into any large dataset do most of the heavy lifting, regardless of which specific samples a model trained on. The framework quantifies how finite datasets shape the denoiser and sampling map, showing that limited data causes models to "overshrink" low-variance directions and pull outputs toward the dataset mean. They validated predictions on both UNet and DiT architectures.
This matters because reproducibility in generative AI has been treated mostly as a practical engineering problem — fix the random seed, pin the weights. This work reframes it as a spectral property of the training data itself, which has real implications for how labs evaluate model diversity and detect memorization. If two models agree because their data share the same statistical fingerprint, that agreement is not evidence of robustness — it is evidence of a shared prior.
The result is a principled baseline, not a cure. Labs chasing genuinely diverse generative outputs may find that swapping datasets is less effective than it looks if the underlying distributions stay similar.