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arXiv · 2602.19512

Variational Trajectory Optimization of Anisotropic Diffusion Schedules

Pengxi Liu·Zeyu Michael Li·Xiang Cheng
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Abstract

We introduce a variational framework for diffusion models with anisotropic noise schedules parameterized by a matrix-valued path $M_t(\theta)$ that allocates noise across subspaces. Central to our framework is a trajectory-level objective that jointly trains the score network and learns $M_t(\theta)$, which encompasses general parameterization classes of matrix-valued noise schedules. We further derive an estimator for the derivative with respect to $\theta$ of the score that enables efficient optimization of the $M_t(\theta)$ 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.

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Pengxi Liu, Zeyu Michael Li, Xiang Cheng. 2026-02-23. Variational Trajectory Optimization of Anisotropic Diffusion Schedules. https://arxiv.org/abs/2602.19512

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