Geometry-Aware Diffusion Guidance via Curvature-Adaptive Tubular Correction

Enze Jiang; Jinwei He; Zheng Ma

cs.CVSep 18, 2026

Geometry-Aware Diffusion Guidance via Curvature-Adaptive Tubular Correction

Authors: Enze Jiang, Jinwei He, Zheng Ma

Organizations: School of Mathematical Sciences Shanghai Jiao Tong University Shanghai, China

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.

Figures & tables

Panel of Figure 1 — Figure 1: CAT within one reverse-diffusion step. The host update can leave the safe region, whereas CAT uses curvature-adaptive normal–tangent allocation to produce $x_{t}^{-}$ inside it.

Task	Type	Method	FFHQ				ImageNet
			PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$
Super-resolution $4\times$	Pixel	DAPS	28.07	0.749	0.2773	76.15	25.54	0.642	0.3759	113.16
		DCDP	26.55	0.765	0.3074	103.17	25.80	0.681	0.3808	128.53
		DDNM	28.80	0.822	0.2435	80.38	26.84	0.743	0.3083	102.82
		DDRM	28.47	0.814	0.2511	84.87	26.43	0.730	0.3175	99.85
		DiffRGD	27.49	0.778	0.2266	64.60	23.96	0.625	0.3687	121.27

Table 1: Main results on FFHQ and ImageNet using 100 images per dataset. Higher PSNR/SSIM and lower LPIPS/FID are better. Bold denotes the best result within each task and type.

Panel of Figure 2 — Figure 2: Qualitative comparison of DPS-based methods on FFHQ across six representative inverse problems. Each panel shows two examples with the same original image and measurement. DPS+CAT denotes DPS equipped with CAT, while DPS+Diffstate is the corresponding DiffState baseline.

Figure 3: Robustness to the guidance step size

\omega

on FFHQ motion deblurring. Each point aggregates 100 images.

Panel of Figure 4 — Figure 4: Qualitative robustness to the guidance step size on FFHQ motion deblurring. Rows correspond to PSLD, PSLD+DiffState, and PSLD+CAT; columns show the ground-truth label, the blurred measurement, and reconstructions obtained with five values of $\omega$ . All entries use the same input image.

Figure 5: Robustness of PSLD+CAT to the tubular-radius coefficient

\rho

on FFHQ motion deblurring. Each point aggregates 100 images, and the horizontal dashed line marks the PSLD result reported in the main experiment.

Panel of Figure 6 — Figure 6: Qualitative robustness of PSLD+CAT to the tubular-radius coefficient on FFHQ motion deblurring. Columns show the ground-truth label, the blurred measurement, the PSLD reconstruction from the main experiment, and PSLD+CAT reconstructions obtained with five values of $\rho$ for the same input.

Figure 7: Robustness to the measurement-noise standard deviation

\sigma_{y}

on FFHQ motion deblurring. Each point aggregates 100 images.

Panel of Figure 8 — Figure 8: Qualitative robustness to measurement noise on FFHQ motion deblurring. The left image shows the ground-truth label. Rows correspond to the four noise levels, while columns show the measurement and reconstructions from each method for the same input image.

Variant	N/T	Curv.	Tube	Armijo	DPS: Nonlinear deblurring				PSLD: Motion deblurring
					PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$
Host	No	No	–	No	17.06	0.326	0.5698	214.46	17.96	0.366	0.6719	374.57
Host + Armijo	No	No	–	Yes	24.08	0.696	0.2751	71.71	25.74	0.695	0.3482	123.15
First-order CAT	Yes	No	1st	Yes	24.26	0.700	0.2718	73.44	25.80	0.699	0.3471	121.86
Tangent-only	Yes	No	Projection	Yes	24.15	0.696	0.2731	75.45	25.61	0.688	0.3504	125.81
CAT w/o Armijo	Yes	Yes	2nd	No	17.33	0.409	0.4555	192.73	19.18	0.413	0.6243	323.10

Table 2: Ablation of CAT on FFHQ using DPS for nonlinear deblurring and PSLD for motion deblurring. Each host and variant are evaluated on 100 images. “1st” and “2nd” denote first- and second-order tube models, respectively. Best results are shown in bold.

Panel of Figure 9 — Figure 9: Qualitative component ablation on FFHQ. The first row uses DPS for nonlinear deblurring, and the second uses PSLD for motion deblurring. Each row shares the same ground truth and measurement across variants.

Study	Setting	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	Memory (MiB)	Time (s)
Sampling steps	DPS	21.97	0.6269	0.3219	85.68	3490	38
	$N=200$	23.50	0.6851	0.2922	82.91	3610	26
	$N=400$	24.62	0.7152	0.2633	70.54	3610	51
	$N=600$	25.42	0.7380	0.2432	64.24	3610	78
	$N=800$	25.92	0.7525	0.2297	58.73	3612	103
	$N=1000$	26.30	0.7623	0.2197	55.17	3612	132

Table 3: Efficiency of DPS+CAT on FFHQ nonlinear deblurring over 100 images using a single NVIDIA GeForce RTX 4090 GPU. Both blocks include the same DPS baseline for reference. The upper block varies the number of reverse sampling steps

N

with Armijo applied at every step, while the lower block fixes

N=1000

and varies the Armijo period

p

. Memory and time denote the recorded GPU memory usage and wall-clock runtime, respectively. Bold marks the best reconstruction quality within each block.

Method	Observation time ratio: 100%				Observation time ratio: 10%
Method	PSNR $\uparrow$	Blur PSNR $\uparrow$	$\widetilde{\chi}^{2}_{\mathrm{cp}}\downarrow$	$\widetilde{\chi}^{2}_{\mathrm{logca}}\downarrow$	PSNR $\uparrow$	Blur PSNR $\uparrow$	$\widetilde{\chi}^{2}_{\mathrm{cp}}\downarrow$	$\widetilde{\chi}^{2}_{\mathrm{logca}}\downarrow$
SMILI	22.67 (3.13)	27.79 (4.02)	1.878 (0.952)	17.612 (10.299)	20.85 (2.90)	25.24 (3.86)	1.209 (0.169)	21.788 (12.491)
EHT-Imaging	24.28 (3.63)	28.57 (4.52)	1.251 (0.250)	1.259 (0.316)	22.67 (3.46)	26.66 (3.93)	1.166 (0.156)	1.240 (0.205)
DPS	25.86 (3.90)	32.94 (6.19)	8.759 (37.784)	5.456 (24.185)	24.36 (3.72)	30.79 (5.75)	13.052 (43.087)	6.614 (26.789)
LGD	21.22 (3.64)	26.06 (4.98)	13.239 (17.231)	13.233 (39.107)	22.08 (3.75)	27.48 (5.09)	10.775 (21.684)	13.375 (56.397)
RED-Diff	23.77 (4.13)	29.13 (6.22)	1.853 (0.938)	2.050 (2.361)	22.53 (3.02)	27.67 (4.53)	2.488 (2.925)	4.916 (13.221)

Table 4: Black hole imaging on InverseBench at

100\%

and

10\%

observation time. Entries are mean (standard deviation). Baseline results are taken from InverseBench [ 24 ] ; DPS+CAT is evaluated on 100 test images. Bold marks the highest mean PSNR/Blur PSNR and the lowest mean reduced chi-squared within each observation setting.

Panel of Figure 10 — Figure 10: Qualitative black hole imaging results for the same ground-truth source from InverseBench at $100\%$ (top) and $10\%$ (bottom) observation time.

Scale $w$	Method	CLIP $\uparrow$	FID $\downarrow$	Sat.	Contrast
10	CFG	31.6905	66.63	0.2901	0.2352
	APG	31.4236	65.26	0.2014	0.1689
	CFG+CAT (ours)	31.2664	64.67	0.2228	0.1943
20	CFG	31.8678	69.85	0.3538	0.2728
	APG	31.7346	67.04	0.2212	0.1865
	CFG+CAT (ours)	31.2742	65.59	0.2263	0.1974

Table 5: Classifier-free text-to-image guidance on 1000 COCO 2017 validation captions. Bold marks the best CLIP and FID at each guidance scale.

Panel of Figure 11 — Figure 11: Qualitative comparison at guidance scale $w=100$ . Within each three-image group, all methods use the same prompt and initial seed. From left to right, the groups correspond to “A bird that is on a tree limb” and “A polar bear dives off a rock into a river.”

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Inverse problem	Host step	$\boldsymbol{\rho}$	$\boldsymbol{p}$	$\boldsymbol{N}$
FFHQ	Random inpainting	$4.0$	$0.1$	$1$	$1000$
	Box inpainting	$2.0$	$0.1$	$1$	$1000$
	Super-resolution	$2.0$	$0.1$	$1$	$1000$
	Motion deblurring	$5.0$	$0.1$	$1$	$1000$
	Gaussian deblurring	$5.0$	$0.1$	$1$	$1000$
	HDR reconstruction	$10.0$	$0.1$	$1$	$1000$

Appendix

Table 6: DPS+CAT and CFG+CAT hyperparameters used in the natural-image, scientific inverse-problem, and text-to-image experiments. The host guidance step corresponds to scale for natural images, step_size for InverseBench, and the CFG scale

w

for COCO. The symbols

\rho

p

, and

N

denote the tubular-radius coefficient, Armijo period, and denoising-step count, respectively. All CFG+CAT runs use a score-norm threshold of

10^{-8}

and 30 bisection iterations with tolerance

10^{-4}

Dataset	Inverse problem	$\boldsymbol{\gamma}$	$\boldsymbol{\omega}$	$\boldsymbol{\rho}$	$\boldsymbol{p}$	$\boldsymbol{N}$
FFHQ	Random inpainting	$0.01$	$2.0$	$1.0$	$1$	$1000$
	Box inpainting	$0.01$	$0.5$	$1.0$	$1$	$1000$
	Super-resolution	$0.01$	$5.0$	$1.0$	$1$	$1000$
	Motion deblurring	$0.01$	$5.0$	$1.0$	$1$	$1000$
	Gaussian deblurring	$0.10$	$10.0$	$1.0$	$1$	$1000$
ImageNet	Random inpainting	$0.10$	$4.0$	$0.1$	$1$	$1000$

Appendix

Table 7: PSLD+CAT hyperparameters used in the main experiments. The original PSLD hyperparameters are the latent data-consistency weight

\gamma

and guidance weight

\omega

; the remaining notation follows Table 6 . PSLD is evaluated on the five linear inverse problems supported by its host implementation.

Dataset	Inverse problem	$\boldsymbol{s_{\mathrm{DPS}}}$	$\boldsymbol{P_{\mathrm{tt}}}$	$\boldsymbol{\rho}$	$\boldsymbol{p}$	$\boldsymbol{N}$
FFHQ	Random inpainting	$15.0$	$10$	$0.1$	$5$	$500$
	Box inpainting	$5.0$	$500$	$0.1$	$5$	$500$
	Super-resolution	$150.0$	$500$	$0.1$	$5$	$500$
	Motion deblurring	$5.0$	$10$	$0.1$	$5$	$500$
	Gaussian deblurring	$10.0$	$10$	$0.1$	$5$	$500$
	HDR reconstruction	$30.0$	$500$	$0.1$	$1$	$500$

Appendix

Table 8: Resample+CAT hyperparameters used in the main experiments.

s_{\mathrm{DPS}}

is the scale of the soft latent DPS step,

P_{\mathrm{tt}}

is the time-travel period, and the remaining notation follows Table 6 .

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