Hyperspectral Diffusion Equivariant Imaging (HyDiff-EI): A Self-supervised Framework for Hyperspectral Image Inpainting

Shuo Li; Mike Davies; Mehrdad Yaghoobi

cs.CVAug 27, 2026

Hyperspectral Diffusion Equivariant Imaging (HyDiff-EI): A Self-supervised Framework for Hyperspectral Image Inpainting

Authors: Shuo Li, Mike Davies, Mehrdad Yaghoobi

Organizations: Institute for Digital Communications, School of Engineering, University of Edinburgh · School of Engineering, University of Edinburgh

Abstract

A novel Hyperspectral diffusion Equivariant Imaging (HyDiff-EI) framework for solving the hyperspectral image (HSI) inpainting problem has been presented here. Unlike conventional diffusion-based methods that rely on large-scale pretraining, HyDiff-EI is a test-time optimization framework that learns directly from a single corrupted HSI acquisition. This makes it flexible for different sensor configurations and particularly well-suited for practical remote sensing scenarios where large annotated hyperspectral datasets are limited. To address the ill-posed nature of unsupervised inpainting, we embed equivariant consistency constraints within the diffusion process. By leveraging the inherent geometric symmetries and intrinsic characteristics of HSIs, HyDiff-EI bridges the gap between generative diffusion modeling and self-consistent physical priors. We empirically show that coupling diffusion modeling with equivariant priors substantially enhances noise robustness and generalizability. Extensive experiments on real-world datasets including Chikusei, Botswana, and EMIT demonstrate that HyDiff-EI offers remarkable inpainting quality over existing self-supervised and diffusion-based algorithms in both noiseless and noisy cases.

Figures & tables

Fig. 1: EI Workflow. $\tilde{\boldsymbol{x}}^{{}^{\prime}}$ and $\tilde{\boldsymbol{x}}^{{}^{\prime\prime}}$ correspond to the right-hand side and left-hand side of Eq. ( 5 ), respectively.

Fig. 2: Flow Chart of the Proposed HyDiff-EI Algorithm. From Left to Right: Noiseless Case and Noisy Case.

Methods	Input	DHP [ 1 ]	R-DLRHyIn [ 3 ]	HIR-Diff [ 22 ]	SHARE [ 34 ]	DDS2M [ 28 ]	HyDiff-EI ( proposed )
MPSNR $\uparrow$	23.401	$29.695\,(\pm 0.53)$	$33.307\,(\pm 0.51)$	$33.862\,(\pm 0.39)$	$34.089\,(\pm 1.03)$	$34.344\,(\pm 0.60)$	$\boldsymbol{35.791}\,(\pm 0.45)$
MSSIM $\uparrow$	0.205	$0.860\,(\pm 0.01)$	$0.906\,(\pm 0.01)$	$0.913\,(\pm 0.01)$	$0.918\,(\pm 0.01)$	$0.921\,(\pm 0.01)$	$\boldsymbol{0.940}\,(\pm 0.01)$
SAM ( ∘ ) $\downarrow$	–	$3.139\,(\pm 0.91)$	$2.790\,(\pm 0.55)$	$3.270\,(\pm 0.55)$	$3.041\,(\pm 0.43)$	$2.264\,(\pm 0.45)$	$\boldsymbol{1.224}\,(\pm 0.47)$
SCC $\uparrow$	–	$0.985\,(\pm 0.01)$	$0.987\,(\pm 0.01)$	$0.984\,(\pm 0.01)$	$0.987\,(\pm 0.01)$	$0.989\,(\pm 0.01)$	$\boldsymbol{0.993}\,(\pm 0.01)$

TABLE I: Comparison between our proposed algorithm and other learning-based inpainting algorithms on the Chikusei and Botswana datasets in the noiseless case. The mean and standard deviation over 20 samples are reported.

Fig. 3: Visual comparison between the proposed HyDiff-EI algorithm and other HSI inpainting methods on the Chikusei dataset and Botswana dataset (noiseless case). All images are visualized at spectral band 100.

Noise Level	Metric	Input	DHP [ 1 ]	DDS2M [ 28 ]	R-DLRHyIn [ 3 ]	HIR-Diff [ 22 ]	SHARE [ 34 ]	HyDiff-EI ( proposed )
$\sigma_{y}=0.1$	MPSNR $\uparrow$	16.797	$27.504\,(\pm 0.77)$	$30.683\,(\pm 0.37)$	$30.848\,(\pm 0.42)$	$31.294\,(\pm 0.39)$	$31.468\,(\pm 0.48)$	$\boldsymbol{31.784}\,(\pm 0.50)$
	MSSIM $\uparrow$	0.167	$0.734\,(\pm 0.02)$	$0.829\,(\pm 0.01)$	$0.837\,(\pm 0.01)$	$0.867\,(\pm 0.01)$	$0.878\,(\pm 0.01)$	$\boldsymbol{0.883}\,(\pm 0.01)$
	SAM ( ∘ ) $\downarrow$	–	$5.193\,(\pm 2.21)$	$17.595\,(\pm 6.98)$	$4.719\,(\pm 2.20)$	$3.727\,(\pm 0.79)$	$3.575\,(\pm 0.74)$	$\boldsymbol{3.432}\,(\pm 0.94)$
	SCC $\uparrow$	–	$0.963\,(\pm 0.05)$	$0.983\,(\pm 0.01)$	$0.964\,(\pm 0.05)$	$\boldsymbol{0.984}\,(\pm 0.01)$	$0.983\,(\pm 0.01)$	$0.984\,(\pm 0.02)$
$\sigma_{y}=0.2$	MPSNR $\uparrow$	14.266	$26.898\,(\pm 0.82)$	$29.012\,(\pm 0.38)$	$28.485\,(\pm 0.42)$	$29.570\,(\pm 0.44)$	$29.564\,(\pm 0.49)$	$\boldsymbol{30.228}\,(\pm 0.62)$
	MSSIM $\uparrow$	0.154	$0.690\,(\pm 0.02)$	$0.761\,(\pm 0.01)$	$0.755\,(\pm 0.01)$	$0.828\,(\pm 0.01)$	$0.840\,(\pm 0.01)$	$\boldsymbol{0.847}\,(\pm 0.01)$

TABLE II: Comparison between our proposed algorithm and other learning-based inpainting algorithms on the Chikusei and Botswana datasets with noise levels

\sigma_{y}=0.1

0.2

, and

0.3

. The mean and standard deviation over 20 samples are reported.

Panel of Figure 6 — Fig. 4: Visual comparison of the proposed HyDiff-EI algorithm with competing methods on the Chikusei and Botswana datasets under a noise level of $\sigma_{y}=0.1$ . All images are visualized at spectral band 100.

Methods	Input	DHP [ 1 ]	R-DLRHyIn [ 3 ]	DDS2M [ 28 ]	HIR-Diff [ 22 ]	SHARE [ 34 ]	HyDiff-EI ( proposed )
MPSNR $\uparrow$	22.517	$31.319\,(\pm 0.74)$	$33.227\,(\pm 0.61)$	$33.358\,(\pm 0.54)$	$33.592\,(\pm 0.48)$	$34.673\,(\pm 0.50)$	$\boldsymbol{35.482}\,(\pm 0.49)$
MSSIM $\uparrow$	0.198	$0.880\,(\pm 0.05)$	$0.878\,(\pm 0.04)$	$0.905\,(\pm 0.01)$	$0.912\,(\pm 0.01)$	$0.920\,(\pm 0.01)$	$\boldsymbol{0.933}\,(\pm 0.01)$
SAM ( ∘ ) $\downarrow$	–	$3.601\,(\pm 0.43)$	$4.397\,(\pm 0.45)$	$3.147\,(\pm 0.47)$	$4.454\,(\pm 0.52)$	$2.782\,(\pm 0.39)$	$\boldsymbol{2.095}\,(\pm 0.42)$
SCC $\uparrow$	–	$0.968\,(\pm 0.00)$	$0.963\,(\pm 0.01)$	$0.974\,(\pm 0.01)$	$0.965\,(\pm 0.00)$	$0.978\,(\pm 0.01)$	$\boldsymbol{0.982}\,(\pm 0.01)$

TABLE III: Comparison between the proposed HyDiff-EI algorithm and other learning-based inpainting methods on the EMIT dataset. The mean and standard deviation over 20 samples are reported.

Panel of Figure 8 — Fig. 6: Comparison of reconstructed spectral signatures at representative inpainted pixels in Chikusei test samples under noiseless and noisy conditions. The left column shows the noiseless results, while the right column shows the noisy results.

Noise Level	Metric	EI	Robust-EI	HyDiff-EI
$\sigma_{y}=0$	MPSNR $\uparrow$	$34.798\,(\pm 0.34)$	$34.806\,(\pm 0.35)$	$\boldsymbol{36.527}\,(\pm 0.36)$
	MSSIM $\uparrow$	$0.895\,(\pm 0.01)$	$0.895\,(\pm 0.01)$	$\boldsymbol{0.904}\,(\pm 0.01)$
$\sigma_{y}=0.1$	MPSNR $\uparrow$	$32.381\,(\pm 0.59)$	$\boldsymbol{34.628}\,(\pm 0.74)$	${34.242}\,(\pm 0.68)$
	MSSIM $\uparrow$	$0.880\,(\pm 0.01)$	$0.892\,(\pm 0.01)$	$\boldsymbol{0.893}\,(\pm 0.01)$
$\sigma_{y}=0.2$	MPSNR $\uparrow$	$31.660\,(\pm 0.77)$	$33.121\,(\pm 0.70)$	$\boldsymbol{33.179}\,(\pm 0.67)$
	MSSIM $\uparrow$	$0.867\,(\pm 0.01)$	$0.874\,(\pm 0.01)$	$\boldsymbol{0.878}\,(\pm 0.01)$

TABLE IV: Performance of EI with and without diffusion on the HSI inpainting task under varying noise levels. Since EI is not originally designed for noisy measurements, Robust-EI is included as a reference for the noisy inpainting setting.

Method	DHP	R-DLRHyIn	HIR-Diff (pre-trained)	DDS2M	SHARE	HyDiff-EI
Time (s/image)	28.12	31.79	53.33	178.43	52.00	38.54
MPSNR (dB) $\uparrow$	28.425	32.464	32.812	33.258	34.108	$\boldsymbol{34.326}$
MSSIM $\uparrow$	0.842	0.889	0.893	0.905	0.911	$\boldsymbol{0.917}$

TABLE V: Time efficiency and performance comparison evaluated on a

144\times 144\times 128

Chikusei sample.

Noise Level	Metric	$\alpha_{EI}=0$	$0.1$	$0.5$	$1$	$2$
$\sigma_{y}=0$	MPSNR $\uparrow$	$28.436$	$30.127$	$33.495$	$\boldsymbol{35.762}$	$33.355$
	MSSIM $\uparrow$	$0.753$	$0.879$	$0.906$	$\boldsymbol{0.932}$	$0.904$
$\sigma_{y}=0.2$	MPSNR $\uparrow$	$15.618$	$27.356$	$30.642$	$\boldsymbol{32.071}$	$28.259$
	MSSIM $\uparrow$	$0.161$	$0.714$	$0.839$	$\boldsymbol{0.891}$	$0.732$

TABLE VI: Quantitative evaluations of HyDiff-EI with different

\alpha_{EI}

Transformation	MPSNR $\uparrow$	MSSIM $\uparrow$
Shifting	$\boldsymbol{34.602}(\pm 0.39)$	$\boldsymbol{0.926}(\pm 0.01)$
Rotation	$34.439(\pm 0.32)$	$0.922(\pm 0.01)$
Scaling	$33.477(\pm 0.25)$	$0.913(\pm 0.01)$
Reflection	$28.334(\pm 0.72)$	$0.836(\pm 0.02)$
Similarity	$33.161(\pm 0.20)$	$0.901(\pm 0.01)$
Affine	$32.104(\pm 0.47)$	$0.898(\pm 0.01)$

TABLE VII: Quantitative evaluations of HyDiff-EI with different types of transformations. The first four are basic transformations, and the last two are projection-based.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Fig. 7: Visual comparison of inpainting results produced by the trained and un-trained HyDiff-EI models.

Panel of Table 14 — TABLE VIII: Inpainting performance of the un-trained HyDiff-EI model and two variants trained on 50 and 300 corrupted HSI samples, respectively, evaluated on a $144\times 144\times 128$ Chikusei sample.

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HIR-ALIGN: Enhancing Hyperspectral Image Restoration via Diffusion-Based Data Generation

Li Pang, Heng Zhao, Yijia Zhang, Deyu Meng+1

Synthetic Data Augmentation Unsupervised Domain Adaptation Hyperspectral Imaging

Open paper AskPDF arXiv

Hyperspectral image (HSI) restoration is crucial for reliable analysis, as real-world HSIs suffer from noise, blur, and resolution loss. However, existing models trained on source data often fail on target domains lacking clean references, a common real-world scenario. To address this, we present HIR-ALIGN, a plug-and-play target-adaptive augmentation framework that enhances HSI restoration by augmenting limited training images with synthetic data matching the target distribution, without extra clean target-domain HSI data. It has three stages: (i) proxy generation, where off-the-shelf restoration models are applied to degraded target observations to produce semantics-preserving proxy HSIs that approximate clean target-domain images; (ii) distribution-adaptive synthesis, where a blur-robust unCLIP diffusion model generates target-aligned RGBs from proxy RGBs with prompt conditioning and embedding-space noise initialization. The warp-based spectral transfer module then synthesizes HSIs by aligning each generated RGB with its proxy RGB, estimating soft patch-wise transport weights, and applying these weights and learnable local interpolation kernels to the proxy HSI; and (iii) aligned supervised finetuning, where restoration networks pretrained on the source distribution are finetuned with proxy HSIs and synthesized target-aligned HSIs, then deployed on degraded target images. We also provide theoretical analysis showing that, under stated assumptions, the proposed augmentation-based finetuning obtains a tighter target-domain restoration-risk upper bound by jointly improving target-distribution coverage and controlling spectral bias. Experiments on simulated and real datasets across denoising, super-resolution, and other restoration tasks demonstrate that HIR-ALIGN is superior to proxy-only target-adaptation baselines and outperforms representative unsupervised methods in most cases.

Abstract

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