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

Zexi Jia, Pengcheng Luo, Zhengyao Fang, Jinchao Zhang, Jie Zhou
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:51857-51877, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-jia26g, title = {Manifold-Optimal Guidance: A Unified {R}iemannian Control View of Diffusion Guidance}, author = {Jia, Zexi and Luo, Pengcheng and Fang, Zhengyao and Zhang, Jinchao and Zhou, Jie}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {51857--51877}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/jia26g/jia26g.pdf}, url = {https://proceedings.mlr.press/v306/jia26g.html}, 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.} }
Endnote
%0 Conference Paper %T Manifold-Optimal Guidance: A Unified Riemannian Control View of Diffusion Guidance %A Zexi Jia %A Pengcheng Luo %A Zhengyao Fang %A Jinchao Zhang %A Jie Zhou %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-jia26g %I PMLR %P 51857--51877 %U https://proceedings.mlr.press/v306/jia26g.html %V 306 %X 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.
APA
Jia, Z., Luo, P., Fang, Z., Zhang, J. & Zhou, J.. (2026). Manifold-Optimal Guidance: A Unified Riemannian Control View of Diffusion Guidance. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:51857-51877 Available from https://proceedings.mlr.press/v306/jia26g.html.

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