PTL-Diffusion

PTL-Diffusion: Diffusion framework with periodic terminal laws for manifold-aware generation

PTL-Diffusion is a new diffusion modeling framework that replaces the standard single Gaussian terminal distribution with a periodic family of Gaussian terminal laws, embedding phase structure directly into the forward noising dynamics rather than only in the denoising network. The authors derive closed-form forward marginals and reverse posteriors for a periodically forced Ornstein-Uhlenbeck process, enabling standard noise-prediction training. Experiments on torus, cylinder, and face datasets show improvements in manifold-level distributional matching over DDPM baselines. The work is a proof-of-concept motivating structured terminal reference laws as a direction for geometry-aware generative modeling.