Variational Trajectory Optimization of Anisotropic Diffusion Schedules

Abstract

We introduce a variational framework for diffusion models with anisotropic noise schedules parameterized by a matrix-valued path $M_t(\hat{I}¸)$ that allocates noise across subspaces. Central to our framework is a trajectory-level objective that jointly trains the score network and learns $M_t(\hat{I}¸)$, which encompasses general parameterization classes of matrix-valued noise schedules. We further derive an estimator for the derivative with respect to $\hat{I}¸$ of the score that enables efficient optimization of the $M_t(\hat{I}¸)$ schedule. For inference, we develop an efficiently-implementable reverse-ODE solver that is an anisotropic generalization of the second-order Heun discretization algorithm. Across CIFAR-10, AFHQv2, FFHQ, and ImageNet-64, our method consistently improves upon the baseline EDM model in all NFE regimes. Code is available at https://github.com/lizeyu090312/anisotropic-diffusion-paper.