Beyond the Semicircle: Free Diffusion Models with Prescribed Equilibria
This research develops a free-probabilistic framework for denoising diffusion models using free probability theory. It proves functional inequalities and convergence properties for processes defined by the free Ornstein–Uhlenbeck diffusion. The work establishes how these models evolve, derives score-matching objectives, and identifies specific equilibrium states, including the Marchenko–Pastur law as a solvable case.