Geometry-Aware Diffusion Guidance via Curvature-Adaptive Tubular Correction

Researchers introduced curvature-adaptive tubular correction (CAT), a training-free plugin that regulates gradient-guided diffusion sampling by decomposing the guidance gradient into normal and tangent components and charging tangent displacement according to directional curvature. Across seven inverse problems on FFHQ and ImageNet, CAT improved the evaluated pixel- and latent-space host samplers, delivered the lowest FID among compared methods at every tested classifier-free guidance scale, and also improved black hole reconstruction on InverseBench. The work, posted as arXiv:2609.21251v1, establishes local guarantees for the tubular approximation, uniqueness of the correction, and sufficient objective decrease.

arXiv:2609.21251v1 Announce Type: new Abstract: 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.