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

• URL: http://arxiv.org/abs/2603.11509v1
• Date: Thu, 12 Mar 2026 03:51:32 GMT
• Title: Manifold-Optimal Guidance: A Unified Riemannian Control View of Diffusion Guidance
• Abstract summary: We present a framework that reformulates guidance as a local optimal control problem.<n>MOG yields a closed-form, geometry-aware update that corrects off-manifold drift without requiring retraining.
• Score: 21.903550549566575
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Information-Theoretic Classifier-Free Guidance with Adaptive Schedule Optimization [15.35957804795103]
  Diffusion models have achieved strong performance in image, text-to-image, and video generation.<n>We propose an information-theoretic framework for CFG schedule optimization.<n>On ImageNet-512 with EDM-XXL and COCO with SD-XL, the learned schedules achieve competitive or improved trade-offs over constant guidance.
  arXiv  Detail & Related papers  (2026-06-23T00:04:04Z)
• Probability-Conserving Flow Guidance [49.03107678763765]
  Adaptive Manifold Guidance (AdaMaG) improves realism, reduces hallucinations, and controlled desaturation in high-guidance.<n>Across image generation benchmarks, AdaMaG improves realism, reduces hallucinations, and controlled desaturation in high-guidance.
  arXiv  Detail & Related papers  (2026-05-19T16:34:01Z)
• Delta Score Matters! Spatial Adaptive Multi Guidance in Diffusion Models [8.570762845568995]
  Diffusion models have achieved remarkable success in synthesizing complex static and temporal visuals.<n>Standard architectures-Free Guidance (CFG) relies on a globally uniform scalar.<n>This amplification traps models in a well-documented "detailartifact dilemma"<n>We propose Spatial Adaptive Multi Guidance (SAMG), a training-free and virtually zero-cost sampling algorithm.
  arXiv  Detail & Related papers  (2026-04-29T10:08:08Z)
• DOC-GS: Dual-Domain Observation and Calibration for Reliable Sparse-View Gaussian Splatting [80.43237927269575]
  In this paper, we revisit sparse-view 3DGS reconstruction from a new perspective.<n>We identify the core challenge as the unobservability of Gaussian primitive reliability.<n>Motivated by this observation, we propose a unified Dual-domain Observation and geometrics in rendered images framework.
  arXiv  Detail & Related papers  (2026-04-08T07:01:24Z)
• Diffusion Controller: Framework, Algorithms and Parameterization [54.82539154511621]
  We present a unified control-theoretic view that casts reverse diffusion sampling as state-only control within (generalized) linearly-solvable Markov Decision Processes.<n>Under this framework, control acts by reweighting the pretrained reverse-time transition kernels, balancing terminal objectives against an $f$-divergence cost.<n>Experiments on Stable Diffusion v1.4 show consistent gains in preference-alignment win rates and improved quality-efficiency trade-offs.
  arXiv  Detail & Related papers  (2026-03-07T01:49:59Z)
• Score-Guided Proximal Projection: A Unified Geometric Framework for Rectified Flow Editing [1.0312968200748118]
  Rectified Flow models achieve state-of-the-art generation quality, yet controlling them for precise tasks remains a challenge.<n>Current approaches bifurcate into inversion-based guidance, which suffers from "geometric locking"<n>We propose Score-Guided Proximal Projection, a unified framework that bridges the gap between deterministic optimization and contraction sampling.
  arXiv  Detail & Related papers  (2026-03-05T23:44:45Z)
• CFG-Ctrl: Control-Based Classifier-Free Diffusion Guidance [31.552164852288325]
  We introduce Sliding Mode Control CFG (SMC-CFG), which enforces the generative flow toward a rapidly convergent sliding manifold.<n>SMC-CFG outperforms standard CFG in semantic alignment and robustness across a wide range of guidance scales.
  arXiv  Detail & Related papers  (2026-03-03T18:59:48Z)
• Riemannian Flow Matching for Disentangled Graph Domain Adaptation [51.98961391065951]
  Graph Domain Adaptation (GDA) typically uses adversarial learning to align graph embeddings in Euclidean space.<n>DisRFM is a geometry-aware GDA framework that unifies embedding and flow-based transport.
  arXiv  Detail & Related papers  (2026-01-31T11:05:35Z)
• Improving Classifier-Free Guidance of Flow Matching via Manifold Projection [3.6087998976768128]
  We provide a principled interpretation of CFG through the lens of optimization.<n>We reformulate the CFG sampling as a homotopy optimization with manifold constraint.<n>Our proposed methods are training-free and consistently refine generation fidelity, prompt alignment, and robustness to the guidance scale.
  arXiv  Detail & Related papers  (2026-01-29T15:49:31Z)
• GeoAda: Efficiently Finetune Geometric Diffusion Models with Equivariant Adapters [61.51810815162003]
  We propose an SE(3)-equivariant adapter framework ( GeoAda) that enables flexible and parameter-efficient fine-tuning for controlled generative tasks.<n>GeoAda preserves the model's geometric consistency while mitigating overfitting and catastrophic forgetting.<n>We demonstrate the wide applicability of GeoAda across diverse geometric control types, including frame control, global control, subgraph control, and a broad range of application domains.
  arXiv  Detail & Related papers  (2025-07-02T18:44:03Z)
• Normalized Attention Guidance: Universal Negative Guidance for Diffusion Models [57.20761595019967]
  We present Normalized Attention Guidance (NAG), an efficient, training-free mechanism that applies extrapolation in attention space with L1-based normalization and refinement.<n>NAG restores effective negative guidance where CFG collapses while maintaining fidelity.<n>NAG generalizes across architectures (UNet, DiT), sampling regimes (few-step, multi-step), and modalities (image, video)
  arXiv  Detail & Related papers  (2025-05-27T13:30:46Z)
• Eliminating Oversaturation and Artifacts of High Guidance Scales in Diffusion Models [27.640009920058187]
  We revisit the CFG update rule and introduce modifications to address this issue.<n>We propose down-weighting the parallel component to achieve high-quality generations without oversaturation.<n>We also introduce a new rescaling momentum method for the CFG update rule based on this insight.
  arXiv  Detail & Related papers  (2024-10-03T12:06:29Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.