High-fidelity unsupervised virtual staining for digital pathology via progressive Schrödinger bridge dynamics

Abstract

Virtual staining converts label-free autofluorescence (AF) images into hematoxylin and eosin (H&E)-like brightfield contrast for nondestructive pathology. We adapt the unpaired neural Schrödinger bridge (UNSB) framework to AF-to-H&E virtual staining and develop an enhanced UNSB (E-UNSB) model for pathology-oriented image translation. E-UNSB retains the unpaired, unidirectional, and progressive stochastic transport formulation of UNSB while introducing pathology-specific structural regularization to preserve cellular morphology and tissue architecture. In particular, saliency constraints and global feature consistency provide multi-scale structural guidance to reduce distortion during staining generation. Experiments demonstrate improved distributional similarity and morphometric consistency over the evaluated unsupervised baselines. Quantitative downstream analysis further indicates that virtual H&E images retain morphometric features relevant to pathological assessment, supporting their potential for high-throughput multimodal tissue analysis.

Keywords

Virtual staining / Unsupervised learning / Schrödinger bridge / Digital pathology / Image processing

References

[1] Abraham T , Shaw A , O'Connor D , et al., 2020. Slide-free MUSE microscopy to H&E histology modality conversion via unpaired image-to-image translation GAN models.https://arxiv.org/abs/2008.08579

[2] Abraham T , Costa PC , Serafini CE , et al., 2023. Label- and slide-free tissue histology using 3D epi-mode quantitative phase imaging and virtual hematoxylin and eosin staining. Optica, 10 (12): 1605- 1618.

[3] Anyi CL , You HZ , Li HK , et al., 2026. Label-free mapping of subcellular dynamics using wide-field interferometric scattering microscopy and spectral exponent analysis. PhotoniX Life, 1: 11.

[4] Bai BJ , Wang HD , Li YZ , et al., 2022. Label-free virtual HER2 immunohistochemical staining of breast tissue using deep learning. BME Front, 2022: 9786242.

[5] Bai BJ , Yang XL , Li YZ , et al., 2023. Deep learning-enabled virtual histological staining of biological samples. Light Sci Appl, 12 (1): 57.

[6] Bankhead P , Loughrey MB , Fernández JA , et al., 2017. QuPath: open source software for digital pathology image analysis. Sci Rep, 7 (1): 16878.

[7] Belaldavar C , Angadi PV , Mudenagudi U , 2024. QuPath for automated analysis of digital images of oral epithelial dysplasia. J Oral Maxillofac Pathol, 28 (3): 381- 386.

[8] Bińkowski M , Sutherland DJ , Arbel M , et al., 2018. Demystifying MMD GANs.https://arxiv.org/abs/1801.01401

[9] Cao R , Nelson SD , Davis S , et al., 2023. Label-free intraoperative histology of bone tissue via deep-learning-assisted ultraviolet photoacoustic microscopy. Nat Biomed Eng, 7 (2): 124- 134.

[10] de Haan K , Zhang YJ , Zuckerman JE , et al., 2021. Deep learning-based transformation of H&E stained tissues into special stains. Nat Commun, 12 (1): 4884.

[11] Feldman AT , Wolfe D , 2014. Tissue processing and hematoxylin and eosin staining. In: Day CE (Ed.), Histopathology: Methods in Molecular Biology. Humana Press, New York, p.31- 43.

[12] Fu H , Gong MM , Wang CH , et al., 2019. Geometry-consistent generative adversarial networks for one-sided unsupervised domain mapping. Proc IEEE/CVF Conf on Computer Vision and Pattern Recognition, p.2422- 2431.

[13] Guo XL , Tao YY , Zhang YZ , et al., 2026. CycleGAN-TMDE:an image dehazing model using cycle generative adversarial network with transmission map and depth estimation. Chin J Electron, 35 (1): 377- 391.

[14] Heusel M , Ramsauer H , Unterthiner T , et al., 2017. GANs trained by a two time-scale update rule converge to a local Nash equilibrium. Proc 31^st Int Conf on Neural Information Processing Systems, p.6629- 6640.

[15] Huang JH , Kou TD , He TY , et al., 2025. Advances in deep learning-based virtual staining of pathological tissues. Laser Optoelectron Prog, 62 (14): 1400001 (in Chinese).

[16] Huang X , Liu MY , Belongie S , et al., 2018. Multimodal unsupervised image-to-image translation. Proc 15_th European Conf on Computer Vision, p.179- 196.

[17] Isola P , Zhu JY , Zhou TH , et al., 2017. Image-to-image translation with conditional adversarial networks. Proc IEEE Conf on Computer Vision and Pattern Recognition, p.5967- 5976.

[18] Karkampouna S , Kruithof-de Julio M , 2023. Dataset EMPaCT TMA.

[19] Kim B , Kwon G , Kim K , et al., 2024. Unpaired image-to-image translation via neural Schrödinger bridge. Proc 12_th Int Conf on Learning Representations.

[20] Kreiss L , Jiang SW , Li X , et al., 2023. Digital staining in optical microscopy using deep learning-a review. PhotoniX, 4 (1): 34.

[21] Li X , 2023. UTOM Dataset: Whole-Slide Pathological Images of Various Kinds of Cancers.

[22] Li XY , Zhang GX , Qiao H , et al., 2021. Unsupervised content-preserving transformation for optical microscopy. Light Sci Appl, 10 (1): 44.

[23] Liu ZJ , Chen LC , Cheng HX , et al., 2024. Virtual formalin-fixed and paraffin-embedded staining of fresh brain tissue via stimulated Raman CycleGAN model. Sci Adv, 10 (13): eadn3426.

[24] Özbey M , Dalmaz O , Dar S , et al., 2023. Unsupervised medical image translation with adversarial diffusion models. IEEE Trans Med Imag, 42 (12): 3524- 3539.

[25] Park T , Efros AA , Zhang R , et al., 2020. Contrastive learning for unpaired image-to-image translation. Proc 16_th European Conf on Computer Vision, p.319- 345.

[26] Pati P , Karkampouna S , Bonollo F , et al., 2024. Accelerating histopathology workflows with generative AI-based virtually multiplexed tumour profiling. Nat Mach Intell, 6 (9): 1077- 1093.

[27] Qiu FH , Zhang YY , Guo XG , et al., 2024. Weakly supervised virtual immunohistochemistry staining via Schrödinger bridge method. Proc IEEE Int Conf on Bioinformatics and Biomedicine, p.2369- 2375.

[28] Rivenson Y , Wang HD , Wei ZS , et al., 2019. Virtual histological staining of unlabelled tissue-autofluorescence images via deep learning. Nat Biomed Eng, 3 (6): 466- 477.

[29] Sun JH , Ye JQ , Chen SY , et al., 2026. Artificial intelligence assisted multi-model pathological diagnosis of breast cancer based on multispectral autofluorescence images. npj Breast Cancer, 12 (1): 62.

[30] Wang JJ , Xiong B , Zhou Y , et al., 2025. VM-GAN:a value mapping framework for virtual staining of optical microscopy images. Opt Expr, 33 (12): 25641- 25655.

[31] Wang Q , Fernandes S , Williams GOS , et al., 2022. Deep learning-assisted co-registration of full-spectral autofluorescence lifetime microscopic images with H&E-stained histology images. Commun Biol, 5 (1): 1119.

[32] Wang XY , Yang S , Zhang J , et al., 2022. Transformer-based unsupervised contrastive learning for histopathological image classification. Med Image Anal, 81: 102559.

[33] Xie SA , Xu YW , Gong MM , et al., 2023. Unpaired image-to-image translation with shortest path regularization. Proc IEEE/CVF Conf on Computer Vision and Pattern Recognition, p.10177- 10187.

[34] Yang XL , Bai BJ , Zhang YJ , et al., 2022. Virtual stain transfer in histology via cascaded deep neural networks. ACS Photon, 9 (9): 3134- 3143.

[35] Ye JQ , Sun JH , 2025. Deep Learning Virtual Staining Dataset: Breast, Mouse, and Organoids.

[36] Zhang RR , E HH , Yuan LF , et al., 2024. FGM-SPCL:open-set recognition network for medical images based on fine-grained data mixture and spatial position constraint loss. Chin J Electron, 33 (4): 1023- 1033.

[37] Zhang SW , Yang B , Yang HP , et al., 2024. Potential rapid intraoperative cancer diagnosis using dynamic full-field optical coherence tomography and deep learning:a prospective cohort study in breast cancer patients. Sci Bull, 69 (11): 1748- 1756.

[38] Zhang YJ , Huang LZ , Pillar N , et al., 2025. Pixel super-resolved virtual staining of label-free tissue using diffusion models. Nat Commun, 16 (1): 5016.

[39] Zhu JY , Park T , Isola P , et al., 2017. Unpaired image-to-image translation using cycle-consistent adversarial networks. Proc IEEE Int Conf on Computer Vision, p.2242- 2251.

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The Authors. Published by Zhejiang University Press Co., Ltd.