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

arXiv: https://arxiv.org/abs/2603.11509 · HTML: https://mlsanity.com/paper/2603.11509/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 32 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 30 of 30)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [Common Diffusion Noise Schedules and Sample Steps are Flawed](https://mlsanity.com/paper/2305.08891/) (2023)
- [Guiding a Diffusion Model with a Bad Version of Itself](https://mlsanity.com/paper/2406.02507/) (2024)
- [Riemannian Score-Based Generative Modelling](https://mlsanity.com/paper/2202.02763/) (2022)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [Lumina-mGPT: Illuminate Flexible Photorealistic Text-to-Image Generation with Multimodal Generative Pretraining](https://mlsanity.com/paper/2408.02657/) (2024)
- [CFG++: Manifold-constrained Classifier Free Guidance for Diffusion Models](https://mlsanity.com/paper/2406.08070/) (2024)
- [Eliminating Oversaturation and Artifacts of High Guidance Scales in Diffusion Models](https://mlsanity.com/paper/2410.02416/) (2024)
- [Guidance with Spherical Gaussian Constraint for Conditional Diffusion](https://mlsanity.com/paper/2402.03201/) (2024)
- [Rethinking the Spatial Inconsistency in Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2404.05384/) (2024)
- [Variational Control for Guidance in Diffusion Models](https://mlsanity.com/paper/2502.03686/) (2025)
- [Optimizing Diffusion Models for Joint Trajectory Prediction and Controllable Generation](https://mlsanity.com/paper/2408.00766/) (2024)
- [Rectified Diffusion Guidance for Conditional Generation](https://mlsanity.com/paper/2410.18737/) (2024)
- [Rethinking Oversaturation in Classifier-Free Guidance via Low Frequency](https://mlsanity.com/paper/2506.21452/) (2025)
- [Manifold-Guided Lyapunov Control with Diffusion Models](https://mlsanity.com/paper/2403.17692/) (2024)

## Abstract (arXiv)

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.