mlsanityData to 14 Oct 2026

Geometry-Aware Diffusion Guidance via Curvature-Adaptive Tubular Correction

arXiv 2609.21251 ↗First posted 18 Sep 2026cs.CVcited by 0

On the map: Diffusion models → Inverse problems and image restoration also fits: 3D, point cloud and scene generation

Abstract (arXiv)

Gradient-guided diffusion samplers provide flexible priors for inverse problems and conditional generation, but strong guidance can move the sampling trajectory into regions where the learned score is poorly supported. Existing tangent-projection strategies limit first-order departure from an iso-density surface, yet discard potentially useful normal motion and overlook the second-order departure induced by tangent motion on a curved surface. We introduce curvature-adaptive tubular correction (CAT), a training-free plugin that regulates both effects within a shared, noise-dependent geometric budget. CAT decomposes the guidance gradient into normal and tangent components, charges normal displacement at first order and tangent displacement according to directional curvature, and obtains their jointly optimal magnitudes from a one-dimensional dual equation. Armijo backtracking calibrates the resulting finite step against the actual guidance objective, while matrix-free directional derivatives avoid constructing the full score Jacobian. We establish local guarantees for the tubular approximation, uniqueness of the correction, and sufficient objective decrease. Across seven inverse problems on FFHQ and ImageNet, CAT improves the evaluated pixel- and latent-space host samplers, with particularly consistent gains in perceptual metrics. It also improves black hole reconstruction on InverseBench and yields the lowest FID among the compared methods at every tested classifier-free guidance scale, while maintaining stable saturation and contrast. These results support curvature-aware tubular control as a reusable mechanism for stabilizing diffusion guidance.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 26 of its 30 references that are in the map. First posted on arXiv 18 Sep 2026.

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26 of 30 references.

Closest ancestors · 13

Same direction, newest first

  1. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences14 Mar
  2. 2024Diffusion State-Guided Projected Gradient for Inverse Problems4 Oct
  3. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing1 Jul
  4. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction25 Mar
  5. 2023Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion1 Dec
  6. 2023Prompt-tuning latent diffusion models for inverse problems2 Oct
  7. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency16 Jul
  8. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models2 Jul
  9. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  10. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  11. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  12. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
1 more
  1. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 13

  1. 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,744
  2. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  3. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  4. 2014Microsoft COCO: Common Objects in Contextcited by 17,608
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  6. 2022Classifier-Free Diffusion Guidancecited by 5,847
  7. 2021Score-based diffusion models for accelerated MRIcited by 311
  8. 2023Manifold Preserving Guided Diffusioncited by 157
  9. 2022Solving 3D Inverse Problems using Pre-trained 2D Diffusion Modelscited by 132
  10. 2024Eliminating Oversaturation and Artifacts of High Guidance Scales in Diffusion Modelscited by 114
  11. 2026Robust Physics-Guided Diffusion for Full-Waveform Inversioncited by 3
  12. 2026Decoupled Latent Optimization of Diffusion Models for Full Waveform Inversioncited by 2
1 more
  1. 2026DiffRGD: An Inference-Time Diffusion Guidance Through Riemannian Gradient Descentcited by 1

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  3. 2026Correcting Guided Diffusion Trajectories with Spectral Alignment
  4. 2025Guided Path Sampling: Steering Diffusion Models Back on Track with Principled Path Guidance
  5. 2026GeoSPRINT: Geometric Redundancy-Aware Step Pruning for Inference in Diffusion Trajectories
  6. 2025Adaptive 3D Reconstruction via Diffusion Priors and Forward Curvature-Matching Likelihood Updates
  7. 2025A-FloPS: Accelerating Diffusion Models via Adaptive Flow Path Sampler
  8. 2024Learning Quantized Adaptive Conditions for Diffusion Models