Manifold-Optimal Guidance: A Unified Riemannian Control View of Diffusion Guidance

TL;DR

This paper introduces Manifold-Optimal Guidance (MOG), a Riemannian control framework that improves diffusion guidance by maintaining trajectories on the data manifold, enhancing fidelity and alignment without retraining or extra computation.

Contribution

The paper proposes MOG, a geometry-aware Riemannian guidance method that corrects off-manifold drift in diffusion models, and Auto-MOG, an adaptive guidance calibration technique.

Findings

MOG outperforms baseline guidance methods in fidelity and alignment.

Auto-MOG eliminates manual hyperparameter tuning.

The approach requires no retraining or significant additional computation.

Abstract

Classifier-Free Guidance (CFG) serves as the de facto control mechanism for conditional diffusion, yet high guidance scales notoriously induce oversaturation, texture artifacts, and structural collapse. We attribute this failure to a geometric mismatch: standard CFG performs Euclidean extrapolation in ambient space, inadvertently driving sampling trajectories off the high-density data manifold. To resolve this, we present Manifold-Optimal Guidance (MOG), a framework that reformulates guidance as a local optimal control problem. MOG yields a closed-form, geometry-aware Riemannian update that corrects off-manifold drift without requiring retraining. Leveraging this perspective, we further introduce Auto-MOG, a dynamic energy-balancing schedule that adaptively calibrates guidance strength, effectively eliminating the need for manual hyperparameter tuning. Extensive validation demonstrates that MOG yields superior fidelity and alignment compared to baselines, with virtually no added computational overhead.