Denoising Diffusions with Optimal Transport: Localization, Curvature, and Multi-Scale Complexity
arXiv:2411.01629v2 Announce Type: replace Abstract: Adding noise is easy; what about denoising? Diffusion is easy; what about reverting a diffusion? Diffusion-based generative models aim to denoise a Langevin diffusion chain, moving from a log-concave equilibrium measure $nu$, say an isotropic Gaussian, back to a complex, possibly non-log-concave initial measure $mu$. The score function performs denoising, moving backward in time, and predicting the conditional mean of the past location given the current one. We show that score denoising is […]