Beyond the Semicircle: Free Diffusion Models with Prescribed Equilibria

Excerpt

arXiv:2510.22778v4 Announce Type: replace-cross Abstract: A growing class of machine-learning objects -- covariance and Gram matrices, kernel and attention matrices, MIMO channel matrices, density operators -- are naturally spectra rather than coordinate vectors. Building a denoising diffusion model for such data by corrupting eigenvalues coordinatewise is not merely elegant: it converges to the wrong limit, because eigenvalues repel rather than move independently. Free probability theory suppli