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Semi-Supervised Virtual Staining via Morphology Preservation and Histopathological Realism Constraints

Baoshun Wang, Weiping Lin, Linwu Wang, Yihuang Hu, Baptiste Magnier, Liansheng Wang

Year: 2026Venue: arXiv preprintArea: cs.CVType: PreprintEmbeddings: 56

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Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 95%

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Summary

The paper proposes a semi-supervised virtual staining framework that utilizes both limited paired histopathological images and abundant unpaired source images. To address the lack of supervision for unpaired data, the method introduces Hessian-derived morphology preservation (HDMP) to maintain tissue structural integrity and histopathological realism constraints (HRC) using a frozen CONCH vision-language model to ensure plausible target-stain characteristics. The framework is evaluated on H&E-to-IHC translation for Ki67 and HER2, as well as FFPE-to-H&E translation, demonstrating improvements in image quality, morphology preservation, and diagnostic performance.

Entities (11)

H&E · stain · 99%IHC · stain · 99%Semi-Supervised Virtual Staining Framework · method · 98%Hessian-derived Morphology Preservation · technique · 97%Histopathological Realism Constraints · technique · 97%HER2 · biomarker · 96%Ki67 · biomarker · 96%CONCH · model · 95%FFPE · sample-type · 94%CycleGAN · model · 90%Pix2Pix · model · 90%

Relation Signals (7)

Histopathological Realism Constraints → basedon → CONCH

confidence 95% · Based on a frozen CONCH vision (a language model [15]), HRC guides generated images

Semi-Supervised Virtual Staining Framework → uses → Hessian-derived Morphology Preservation

confidence 95% · we propose a stable semi-supervised virtual staining framework that jointly exploits... Hessian-derived morphology preservation extracts structural cues

Semi-Supervised Virtual Staining Framework → uses → Histopathological Realism Constraints

confidence 95% · Histopathological realism constraints further guide the output toward plausible target-stain characteristics

Semi-Supervised Virtual Staining Framework → evaluatedon → H&E-to-IHC translation for Ki67

confidence 92% · Extensive experiments on H&E-to-IHC translation for Ki67 and HER2

Semi-Supervised Virtual Staining Framework → evaluatedon → H&E-to-IHC translation for HER2

confidence 92% · Extensive experiments on H&E-to-IHC translation for Ki67 and HER2

Semi-Supervised Virtual Staining Framework → evaluatedon → FFPE-to-H&E translation

confidence 92% · as well as FFPE-to-H&E translation

Hessian-derived Morphology Preservation → extractsfrom → Source Image

confidence 90% · Hessian-derived morphology preservation extracts structural cues from each source image

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Abstract

Abstract:Virtual staining aims to computationally generate target-stained histopathological images while reducing the cost and time associated with conventional staining procedures. However, existing methods rely predominantly on strictly paired and accurately registered training data, which are difficult and expensive to obtain in routine practice. To reduce this dependence, we propose a stable semi-supervised virtual staining framework that jointly exploits both limited paired data and abundant unpaired source images. Directly incorporating unpaired images is challenging because their generated results lack corresponding targets for supervision, potentially leading to unrealistic staining, morphological degradation, or even training collapse. To obtain reliable supervision from these images, Hessian-derived morphology preservation extracts structural cues from each source image and constrains the generated output to retain tissue morphology. Histopathological realism constraints further guide the output toward plausible target-stain characteristics, preventing the source-derived structural supervision from degenerating into contour enhancement or simple color transformation. Together, the two components suppress structural and appearance drift, stabilize semi-supervised stain translation, and promote the preservation of diagnostically relevant information. Extensive experiments on H&E-to-IHC translation for Ki67 and HER2, as well as FFPE-to-H&E translation, demonstrate consistent improvements in image quality, morphology preservation, robustness, and downstream diagnostic performance. Code will be available.

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Semi-Supervised Virtual Staining via Morphology Preservation and Histopathological Realism Constraints Baoshun Wang Weiping Lin Linwu Wang Yihuang Hu Baptiste Magnier Liansheng Wang †thanks: This work was supported by the National Natural Science Foundation of China under Grant 62371409, Fujian Provincial Natural Science Foundation of China under Grant 2023J01005. (Corresponding author: Liansheng Wang.)†thanks: Baoshun Wang and Weiping Lin contributed equally.†thanks: Baoshun Wang, Weiping Lin, Linwu Wang, Yihuang Hu and Liansheng Wang are with Department of Computer Science, School of Informatics, Xiamen University, Xiamen 361005, China (e-mail: bswang, wplin, lwwang, huyihuang@stu.xmu.edu.cn; lswang@xmu.edu.cn).†thanks: Baptiste Magnier is with EuroMov Digital Health in Motion, Univ Montpellier, IMT Mines Ales, Ales, France, and also with Service de Médecine Nucléaire, Centre Hospitalier Universitaire de Nîmes, Université de Montpellier, Nîmes, France (e-mail: baptiste.magnier@mines-ales.fr). Abstract Virtual staining aims to computationally generate target-stained histopathological images while reducing the cost and time associated with conventional staining procedures. However, existing methods rely predominantly on strictly paired and accurately registered training data, which are difficult and expensive to obtain in routine practice. To reduce this dependence, we propose a stable semi-supervised virtual staining framework that jointly exploits both limited paired data and abundant unpaired source images. Directly incorporating unpaired images is challenging because their generated results lack corresponding targets for supervision, potentially leading to unrealistic staining, morphological degradation, or even training collapse. To obtain reliable supervision from these images, Hessian-derived morphology preservation extracts structural cues from each source image and constrains the generated output to retain tissue morphology. Histopathological realism constraints further guide the output toward plausible target-stain characteristics, preventing the source-derived structural supervision from degenerating into contour enhancement or simple color transformation. Together, the two components suppress structural and appearance drift, stabilize semi-supervised stain translation, and promote the preservation of diagnostically relevant information. Extensive experiments on H&E-to-IHC translation for Ki67 and HER2, as well as FFPE-to-H&E translation, demonstrate consistent improvements in image quality, morphology preservation, robustness, and downstream diagnostic performance. Code will be available. Index Terms: Computational pathology, Morphology preservation, Histopathological realism constraints, Semi-supervised learning, Virtual staining I Introduction Histopathological staining reveals tissue characteristics that are essential for disease diagnosis and treatment planning. Hematoxylin and eosin (H&E) staining primarily presents tissue organization, cellular morphology, and nuclear appearance [1], whereas immunohistochemistry (IHC) visualizes the expression and spatial distribution of specific biomarkers, such as HER2 and Ki67 [2]. These complementary staining patterns provide important evidence for tumor characterization and therapeutic decision-making. Conventional staining, however, involves multiple tissue-processing and chemical procedures, resulting in substantial labor, reagent consumption, and turnaround time. These limitations have motivated computational methods that generate a desired staining modality directly from an available pathological image, including conditional generative adversarial networks [3, 4]. Fig. 1: Motivation of the proposed framework. (a) Limited paired data constrain virtual staining performance. (b) Unpaired source images improve data utilization but lack direct cross-stain supervision. (c) Hessian-derived morphology preservation extracts structural supervision from source images, while histopathological realism constraints promote realistic target staining. With the digitization of pathological slides, virtual staining has emerged as a computational approach for translating tissue images between staining modalities [5]. Unpaired image-to-image translation methods, such as CycleGAN, CUT, and pathology-specific stain-transfer models, learn from independently collected source- and target-domain images without exact spatial correspondence [6, 7, 8]. This flexibility is attractive in pathology, where corresponding tissue sections are often unavailable. Nevertheless, virtual staining is not simply a style-transfer problem. A visually realistic image is insufficient if tissue boundaries are distorted or biomarker-related staining appears in inappropriate regions. Because distribution-level matching cannot determine the correct local relationship between source tissue and target staining, paired supervision remains important for preserving morphology and diagnostically relevant staining patterns. Accordingly, supervised models such as Pix2Pix and Pix2PixHD remain widely used foundations for virtual staining [9, 10]. The reliability of paired supervision comes with a substantial data-acquisition burden. Cross-stain image pairs are commonly obtained from adjacent tissue sections or from tissue imaged before and after staining. Tissue deformation, missing regions, sectioning artifacts, staining variations, and registration errors can disrupt their spatial correspondence. Constructing a high-quality paired dataset therefore requires extensive registration, meticulous manual inspection, and exclusion of poorly aligned samples. Consequently, only a limited proportion of collected images can be retained as registered source–target pairs, whereas many independently acquired source-domain images remain available without corresponding target stains. Semi-supervised learning has achieved considerable success in medical image classification, segmentation, and related tasks by combining limited annotated data with additional unannotated samples [11, 12, 13, 14]. This paradigm is particularly promising for virtual staining because paired images are difficult to acquire, while unpaired source images are abundant. In this work, unpaired images refer specifically to source-domain images without corresponding target-stain images. Paired samples provide direct cross-stain supervision, including tissue correspondence and target-specific staining information, whereas unpaired samples increase the diversity of tissue appearances available during training. Exploiting unpaired images in a generative task is nevertheless challenging. Unlike classification or segmentation, virtual staining must predict a high-dimensional target image, and an unpaired input provides no corresponding target with which to verify the generated result. Without appropriate supervision, the generator may deviate from the intended stain mapping, distort source-tissue morphology, produce unrealistic target staining, or even collapse during training. Consequently, reliable supervision must therefore be derived for unpaired samples without requiring additional target images. To this end, we first introduce Hessian-derived morphology preservation to extract structural supervision directly from each source image. Second-order spatial responses capture morphology-related transitions around tissue interfaces, cellular boundaries, and nuclear contours and can be compared across staining modalities. This source-derived signal therefore constrains tissue morphology even when a paired target is unavailable. However, morphology preservation alone may encourage the generator to overemphasize contours or reduce stain translation to a simple color transformation, without ensuring a realistic target-stain appearance. We consequently introduce histopathological realism constraints (HRC) as a complementary source of supervision. Based on a frozen CONCH vision (a language model [15]), HRC guides generated images toward plausible target-stain characteristics. For paired samples, the corresponding target image provides additional cross-stain representation guidance; for unpaired samples, the target-stain prompt serves as a stable reference. HRC therefore complements the source-derived morphology supervision and discourages structure-only shortcuts. Together, HRC and morphology preservation regulate both target-stain realism and source-tissue morphology, thereby stabilizing semi-supervised optimization and promoting the preservation of diagnostically relevant information. The proposed framework uses a shared generator for paired and unpaired samples. Paired samples are optimized using conventional cross-stain supervision together with HRC and morphology preservation, whereas unpaired samples obtain supervision from the latter two components. We evaluate the framework on H&E-to-IHC virtual staining for Ki67 and HER2, as well as FFPE-to-H&E translation, under different unpaired-to-paired data ratios. The evaluation covers image quality, morphology preservation, pathology-informed measurements, robustness, and downstream diagnostic performance. The main contributions of this work are summarized as: • We propose a stable semi-supervised virtual staining framework that jointly exploits limited registered source–target pairs and abundant unpaired source images, addressing optimization instability caused by the absence of corresponding targets. • We introduce Hessian-derived morphology preservation, which obtains structural supervision directly from source images and reduces alterations to tissue interfaces, cellular boundaries, and nuclear contours during stain translation. • We develop histopathological realism constraints based on a frozen CONCH model to promote plausible target-stain characteristics and prevent source-derived structural supervision from degenerating into contour enhancement or simple color transformation. • We validate the proposed framework on three virtual staining tasks under different unpaired-to-paired data ratios, demonstrating improvements in staining quality, morphology preservation, robustness, and downstream diagnostic performance. I Related Work I-A Virtual Staining Virtual staining computationally translates pathological images from one staining modality to another. Existing approaches can generally be categorized according to whether spatially corresponding cross-stain images are available during training. Unpaired methods learn from independently collected both source- and target-domain images without requiring spatial registration. CycleGAN uses cycle consistency to encourage content preservation, whereas CUT maintains correspondence between input and output representations through contrastive learning [6, 7]. Although these approaches reduce the need for paired data, their supervision is mainly derived from domain-level distribution matching or representation consistency. They may therefore reproduce a realistic target-domain appearance without guaranteeing correct biomarker localization or faithful morphology preservation. Paired methods use registered source–target images to directly supervise the desired stain mapping. Pix2Pix and Pix2PixHD combine reconstruction and adversarial objectives and remain common supervised backbones [9, 10]. Subsequent studies have explored multi-scale and high-resolution generation [16, 17, 18]; adaptive, weakly supervised, or weakly paired learning [19, 20, 21]; pathology-informed objectives [22, 23]; diffusion-based stain transfer [24, 25]; virtual multiplexing [26]; and foundation model-guided translation [27]. These methods provide effective cross-stain supervision, but their dependence on registered or approximately corresponding images limits the scale and diversity of available training data. I-B Semi-supervised Learning for Medical Image Translation Semi-supervised learning combines a small collection of annotated data with a larger set of unannotated samples and has been widely studied in medical image classification, segmentation, and domain adaptation [11, 12, 13]. Representative strategies include consistency regularization [28, 29], pseudo-labeling [30], and contrastive representation learning [31]. Most semi-supervised methods are designed for tasks with constrained output spaces. In classification and segmentation, predictions on unannotated samples can be converted into categorical or pixel-wise supervision. Image translation is more difficult because the model must synthesize a high-dimensional output for which multiple appearances may seem plausible. An inaccurate generated image can therefore be reinforced during optimization and gradually shift the learned mapping away from the intended target domain. This problem is particularly important in virtual staining, where the output must simultaneously exhibit preserve the spatial organization of the source tissue and realistic target-stain characteristics. For an unpaired source image, neither cross-stain morphology nor target-stain appearance can be directly verified using a corresponding target. Semi-supervised virtual staining therefore requires task-specific supervision that can be obtained without additional paired images. I-C Morphology Preservation and Histopathological Realism Morphology preservation is fundamental in virtual staining, as tissue architecture and cellular boundaries must remain spatially consistent across modalities [9, 10]. For paired data, reconstruction and perceptual objectives provide direct structural supervision [32]. However, unpaired source images lack corresponding targets, complicating morphological fidelity in semi-supervised learning [11, 12]. To address this, our framework uses Hessian-derived morphology preservation to extract structural constraints directly from the unpaired source images. Yet, relying solely on source-derived morphological constraints can trigger optimization shortcuts [33]. Without explicit target-appearance guidance, the model may default to superficial color transformations or hallucinate contour-dominated features [34]. Thus, histopathological realism constraints are necessary to ensure plausible target staining. Although pathology foundation models capture rich diagnostic concepts [23, 27, 35], their use as fixed references for target-stain realism in semi-supervised translation remains largely underexplored. Our dual-pathway approach resolves these complementary needs. Hessian-derived preservation ensures source-side spatial consistency, while realism constraints provide target-side semantic guidance. This interaction prevents the structural supervision from degrading into simple color-mapping. Ultimately, this synergy enables stable semi-supervised virtual staining that preserves both source morphology and target diagnostic semantics. The methodology follows below. I Methodology I-A Problem Formulation Let S and T denote the source- and target-staining domains, respectively. Virtual staining aims to learn a generator called G:S→TG:S→ T that maps a source-domain image to its corresponding target-stained image. Then, we consider a paired dataset composed of registered source–target images: Dp=(si,ti)i=1Np,D_p= \(s_i,t_i) \_i=1^N_p, (1) where si∈Ss_i∈ S and ti∈Tt_i∈ T. Given a paired source image, the generator produces: t^i=G⁡(si), t_i=G(s_i), (2) which can be directly supervised by the corresponding target tit_i. Such paired samples provide cross-stain supervision for both tissue correspondence and target-specific staining characteristics. Additionally, we use a collection of unpaired source images: Du=ujj=1Nu,D_u= \u_j \_j=1^N_u, (3) where uj∈Su_j∈ S has no corresponding target-stain image. Its generated result is denoted by: t^ju=G⁡(uj). t_j^u=G(u_j). (4) Here, unpaired specifically refers to source-domain images without corresponding target images. Our objective is to learn the cross-stain mapping from DpD_p while deriving reliable supervision for DuD_u from the source morphology and the expected target-stain appearance. Fig. 2: Overview of the proposed semi-supervised virtual staining framework. (a) Hessian-derived morphology preservation (HDMP) extracts structural supervision from each source image and constrains the generated output to retain source-tissue morphology. (b) Histopathological realism constraints (HRC) use a frozen CONCH model to guide the output toward plausible target-stain characteristics, with additional target-image alignment when a paired target is available. (c) The two supervisory pathways jointly constrain the shared generator. Paired samples additionally receive direct cross-stain supervision, whereas unpaired samples are optimized without corresponding target images. I-B Framework Overview As illustrated in Fig. 2, the proposed framework contains paired and unpaired branches that share the same generator. Their difference lies in the available sources of supervision. For a paired sample (si,ti)(s_i,t_i), the corresponding target tit_i provides direct cross-stain supervision for the generated image t^i t_i. The paired branch additionally employs Hessian-derived morphology preservation (HDMP) and histopathological realism constraints (HRC) to reinforce source-tissue consistency and target-stain realism. For an unpaired source image uju_j, neither pixel-level translation supervision nor alignment with a corresponding target image is available. We therefore construct two complementary supervisory pathways. HDMP extracts structural information directly from uju_j, providing source-side supervision without requiring a target image. HRC supplies a target-side reference through the frozen CONCH model and encourages t^ju t_j^u to exhibit plausible target-stain characteristics. The two methods are jointly required. HDMP specifies which tissue structures should remain spatially consistent, but by itself may overemphasize contours or encourage a simple color transformation. HRC specifies what the generated target staining should look like and discourages such structure-only shortcuts. Their interaction provides complementary source-side and target-side supervision for stable learning from unpaired images. I-C Hessian-Derived Morphology Preservation An unpaired source image provides no corresponding target from which structural consistency can be directly evaluated. Nevertheless, the source image itself contains tissue architecture and cellular organization that should remain spatially consistent after stain translation. We therefore derive morphology supervision directly from each source image. Rapid local intensity changes in pathological images commonly occur around tissue interfaces, glandular boundaries, cellular contours, and nuclear edges. These structures can be characterized using second-order spatial responses and compared between source and generated images despite their different staining appearances. For an image I, we first obtain its grayscale representation through a fixed transformation ⁡(⋅)G(·). Its Hessian-derived response is defined as: R⁡(I)=tr⁡(∇2(I)),R(I)=tr (∇^2G(I) ), (5) where ∇2∇^2 denotes the spatial Hessian and tr⁡(⋅)tr(·) denotes its trace. Thereafter, for a two-dimensional image I: R⁡(I)=∂2⁡(I)∂x2+∂2⁡(I)∂y2.R(I)= ∂^2G(I)∂ x^2+ ∂^2G(I)∂ y^2. (6) As shown in Fig. 3, grayscale conversion reduces direct dependence on individual color channels, while the Hessian-derived response emphasizes morphology-related structures around tissue interfaces, cellular contours, and nuclear boundaries. The overlay is shown only for visualization, whereas the loss is computed from the original signed response maps. Fig. 3: Visualization of the Hessian-derived morphology map. A representative pathological region is converted to grayscale and processed using the fixed Hessian-trace operator. Strong responses are mainly observed around tissue interfaces, cellular contours, and nuclear boundaries. The overlay is shown only for visualization. Morphology preservation compares the response of each generated image with that of its original source image. Hence, for a paired sample: Lmorp=‖R⁡(t^i)−R⁡(si)‖1.L_mor^p= \|R( t_i)-R(s_i) \|_1. (7) On the contrary, for an unpaired source image: Lmoru=‖R⁡(t^ju)−R⁡(uj)‖1.L_mor^u= \|R( t_j^u)-R(u_j) \|_1. (8) Unlike direct RGB reconstruction, this method does not require the source and generated images to share the same staining appearance. Instead, it transfers morphology-related supervision from the source image to the generated result, reducing changes to tissue interfaces, cellular boundaries, and nuclear contours. Morphology preservation alone, however, does not determine whether the generated image exhibits realistic target staining. Excessive reliance on the source-derived response may produce contour-dominated outputs or reduce translation to a superficial color transformation. A complementary target-side constraint is therefore required. I-D Histopathological Realism Constraints To complement the source-derived morphology supervision, we introduce histopathological realism constraints based on the frozen CONCH vision–language model. HRC guides generated images toward plausible target-stain appearances and modality-specific staining characteristics. A task-specific textual prompt P describes the expected appearance and characteristic staining pattern of the target modality. Its normalized text representation is zT=ET(P)‖ET(P)‖2,z_T= E_T(P) \|E_T(P) \|_2, (9) where ET(⋅)E_T(·) denotes the frozen CONCH text encoder. Given a generated image t t, its normalized visual representation is given by: zI(t^)=EI(t^)‖EI(t^)‖2,z_I( t)= E_I( t) \|E_I( t) \|_2, (10) where EI(⋅)E_I(·) denotes the frozen CONCH image encoder. The image–text realism constraint is defined as: LIT(t^,P)=log⁡[1+exp⁡(−zI(t^)⊤zTτ)],L_IT( t,P)= [1+ (- z_I( t) z_Tτ ) ], (11) where τ is a temperature parameter. This objective encourages the generated representation to remain compatible with the expected target-stain characteristics. I-D1 Paired Realism Constraint For a paired sample (si,ti)(s_i,t_i), the textual reference is supplemented with sample-specific guidance from the corresponding target image. Its normalized representation is: zR(ti)=EI(ti)‖EI(ti)‖2.z_R(t_i)= E_I(t_i) \|E_I(t_i) \|_2. (12) The image–image alignment constraint is defined as: LIIp=‖zI(t^i)−zR(ti)‖22.L_I^p= \|z_I( t_i)-z_R(t_i) \|_2^2. (13) The complete HRC objective for the paired branch is: Lrealp=LIT(t^i,P)+λfLIIp.L_real^p=L_IT( t_i,P)+ _fL_I^p. (14) The image–text term provides a general reference for the expected target-stain appearance, whereas image–image alignment supplies sample-specific cross-stain information from the corresponding real target. I-D2 Unpaired Realism Constraint For an unpaired source image uju_j, no corresponding target is available for image–image alignment. HRC therefore relies on the target-stain prompt: Lrealu=LIT(t^ju,P).L_real^u=L_IT( t_j^u,P). (15) Because both CONCH encoders remain frozen, the target-stain reference does not change during generator optimization. This stable reference reduces appearance drift and complements the morphology supervision derived from the source image. Together, they discourage both structurally distorted results and contour-preserving but unrealistic stain transformations. I-E Training Objective For a paired sample, the conventional image-to-image translation objective is computed by: Ltrans=LGAN+λrecLrec.L_trans=L_GAN+ _recL_rec. (16) The complete paired-branch objective combines direct cross-stain supervision, morphology preservation, and histopathological realism constraints by: Lp=Ltrans+λmLmorp+λrLHRCp.L_p=L_trans+ _mL_mor^p+ _rL_HRC^p. (17) For an unpaired source image, no direct translation loss or target-image alignment can be computed. Its objective becomes therefore: Lu=λmLmoru+λrLrealu.L_u= _mL_mor^u+ _rL_real^u. (18) The mini-batch objective is selected according to the availability of corresponding target images: L=Lp,for a paired batch,Lu,for an unpaired batch.L= casesL_p,&for a paired batch,\\[5.69054pt] L_u,&for an unpaired batch. cases (19) In practice, the generator is first warmed up using paired samples, after which the unpaired branch is activated. This schedule prevents unpaired optimization from being introduced before a basic cross-stain mapping has been established. The activation point and loss-weight settings are provided in the Sec. Implementation Details. The proposed methods introduce complementary training signals without modifying the generator architecture. IV Experiments IV-A Datasets We evaluate the proposed framework on three virtual staining tasks: H&E-to-IHC virtual staining for Ki67 and HER2, and FFPE-to-H&E translation. For each task, accurately registered source–target pairs provide paired supervision, while additional unpaired source images are incorporated during semi-supervised training. IV-A1 H&E-to-IHC Virtual Staining for Ki67 The paired data are selected from the public MIST-Ki67 dataset. To ensure reliable supervision, we retain only image pairs with satisfactory registration quality, resulting in 2,000 pairs for training and 1,000 pairs for testing. In addition, 10,000 source-domain patches from the Ki67 subset of the public IHC4BC dataset are used as unpaired source images. IV-A2 H&E-to-IHC Virtual Staining for HER2 We use a private paired dataset, self-HER2, constructed from 30 H&E–HER2 IHC WSI pairs stained with the 4B5 antibody and covering HER2 scores of 0, 1+, 2+, and 3+. Following WSI registration using Gatenbee et al.’s method [36], patch extraction at 1024×10241024× 1024 pixels, and manual quality control, 3,000 registered pairs are retained, including 2,500 for training and 500 for testing. Additionally, 10,000 source-domain patches from the HER2 subset of IHC4BC are used as unpaired source images. IV-A3 FFPE-to-H&E Translation For FFPE-to-H&E translation, we use a private paired dataset, self-FFPE. Following WSI registration and manual quality control, 2,500 registered pairs are retained for training and 1,000 pairs for testing. A separate private dataset, self-FFPE2, provides 7,500 unpaired FFPE patches for semi-supervised training. IV-B Implementation Details Unless otherwise specified, the unpaired-to-paired data ratio is set to 2:1, and all models are trained for 100 epochs. The generator is first warmed up using paired samples for 70 epochs, after which unpaired samples are introduced for the remaining 30 epochs. For Hessian-derived morphology preservation, RGB images are converted to grayscale using 0.299R+0.587G+0.114B0.299R+0.587G+0.114B and processed with a fixed four-neighbor Laplacian kernel [0101−41010] [ smallmatrix0&1&0\\ 1&-4&1\\ 0&1&0 smallmatrix ]. The loss is computed from the raw signed responses, while display enhancement is used only for visualization. For comparison with Pix2PixHD, the generator backbone, optimizer, and total number of training epochs are kept identical. Other methods follow their official implementations and use the same data splits. All experiments are conducted on eight NVIDIA RTX 3090 GPUs with 24 GB memory each. IV-C Comparison Methods We compare the proposed method with representative virtual staining approaches, including Pix2Pix, Pix2PixHD, ASP, PyramidPix2Pix, TDKStain, HistDiST, and UNIStainNet. These methods cover supervised image-to-image translation, weakly paired learning, diffusion-based generation, and pathology foundation model-based approaches. We additionally combine the proposed framework with Pix2PixHD to evaluate its effect under the same generator backbone. TDKStain and HistDiST are specifically designed for H&E-to-IHC translation and are therefore evaluated only on the H&E-to-IHC datasets. IV-D Evaluation Protocol We evaluate the generated images from three complementary perspectives: image-level quality, stain-specific agreement, and downstream diagnostic utility. IV-D1 Image-Level Quality PSNR, SSIM, and MS-SSIM measure pixel-level and structural agreement between generated and reference images. DISTS evaluates perceptual similarity, while FID and KID measure distributional agreement. IV-D2 Stain-Specific Assessment For H&E-to-IHC virtual staining, DAB-KL and integrated optical density difference (IOD-D) are used to assess biomarker-related staining. Generated and real IHC images are decomposed to obtain their DAB channels. DAB-KL measures the divergence between their DAB distributions, whereas IOD-D measures the difference in total DAB-positive staining intensity. Lower values indicate closer agreement with the real IHC images. For FFPE-to-H&E translation, generated and real images are transformed into the HED color space. Dice scores computed from the hematoxylin and eosin channels, denoted as H-Dice and E-Dice, evaluate the agreement of nuclei-related and eosin-stained tissue regions, respectively. IV-D3 Downstream Diagnostic Evaluation For H&E-to-IHC virtual staining, we further examine whether generated IHC images preserve information required for four-class HER2 scoring. The evaluation is conducted on an external dataset with HER2 annotations. Original H&E images and real IHC images are included as lower- and upper-reference inputs, respectively. IV-E Main Results IV-E1 Comparison with Baselines and SOTA Methods The quantitative results are reported in Tables I and I. Across H&E-to-IHC virtual staining for HER2 and Ki67, as well as FFPE-to-H&E translation, incorporating the proposed framework consistently improves Pix2PixHD across image-level, distributional, and stain-specific evaluations. Compared with representative virtual staining methods, our framework achieves competitive or superior performance across the three tasks, with improvements extending beyond visual similarity to biomarker-related staining and tissue-component agreement. Representative results are shown in Fig. 7. Our method produces more plausible target-stain appearances while better retaining tissue organization and cellular structures. These results reveal the complementary roles of the two proposed methods: Hessian-derived morphology preservation transfers structural supervision from the source image, while histopathological realism constraints prevent the translation from degenerating into contour enhancement or superficial color transformation. IV-E2 Downstream Diagnostic Evaluation To evaluate whether the generated IHC images preserve diagnostically relevant information, we conduct a downstream four-class HER2 scoring experiment on an external dataset with explicit HER2 annotations. Original H&E images and real IHC images are included as lower- and upper-reference inputs, respectively, while the remaining settings use virtual IHC images generated by different methods. As shown in Fig. 4, the proposed method achieves the strongest overall HER2 scoring performance among the compared virtual staining methods. This result indicates that the generated images exhibit realistic staining appearances while preserving HER2-related information useful for downstream diagnostic assessment. TABLE I: Quantitative comparison on H&E-to-IHC virtual staining for HER2 and Ki67 using the self-HER2 and MIST-Ki67 test sets. Image-Level Agreement Perceptual / Distributional Quality Stain-Specific Agreement PSNR↑ SSIM↑ MSSSIM↑ FID↓ KID↓ DISTS↓ DAB-KL↓ IOD-D↓ Self-HER2 ASP 16.38 0.2304 0.2735 155.6165 0.1459 0.2847 0.5660 0.0263 PyramidPix2Pix 17.95 0.3387 0.3746 90.1506 0.0680 0.2545 0.3868 0.0243 TDKStain 17.89 0.3465 0.3653 64.7646 0.0298 0.2954 0.3812 0.0255 HistDiST 18.14 0.3345 0.3694 56.0305 0.0245 0.2542 0.4599 0.0269 UNIStainNet 17.82 0.3528 0.3870 59.4592 0.0259 0.2418 0.4180 0.0256 Pix2Pix 17.92 0.3487 0.3854 79.8819 0.0503 0.2423 0.4116 0.0246 Pix2PixHD 18.39 0.3321 0.3726 87.6770 0.0660 0.2807 0.4773 0.0251 Pix2PixHD w/ ours 18.60 0.3704 0.4029 52.4523 0.0249 0.2335 0.3659 0.0240 MIST-Ki67 ASP 14.60 0.2299 0.1836 51.1829 0.0295 0.2438 0.5622 0.0363 PyramidPix2Pix 14.23 0.2287 0.1698 91.3043 0.0790 0.2611 0.5113 0.0331 TDKStain 14.47 0.2388 0.1802 55.7503 0.0347 0.2374 0.4990 0.0313 HistDiST 14.41 0.2355 0.1868 77.8673 0.0480 0.2818 0.8274 0.0425 UNIStainNet 14.50 0.1858 0.1741 54.5161 0.0323 0.3020 0.5490 0.0389 Pix2Pix 13.79 0.2462 0.1827 78.0272 0.0538 0.2634 0.5969 0.0430 Pix2PixHD 14.21 0.2356 0.1727 114.7570 0.0936 0.2871 0.5827 0.0377 Pix2PixHD w/ ours 14.90 0.2651 0.2122 47.2794 0.0277 0.2595 0.4969 0.0305 TABLE I: Quantitative comparison on FFPE-to-H&E translation using the self-FFPE test set. Image-Level Agreement Perceptual / Distributional Quality Stain-Specific Agreement PSNR↑ SSIM↑ MSSSIM↑ FID↓ KID↓ DISTS↓ H-Dice↑ E-Dice↑ Self-FFPE ASP 15.79 0.3583 0.3632 97.6618 0.0640 0.2895 0.1984 0.7604 PyramidPix2Pix 17.59 0.4852 0.6577 23.1832 0.0043 0.1422 0.5454 0.6749 UNIStainNet 18.15 0.5228 0.6892 19.5909 0.0017 0.2267 0.5893 0.7387 Pix2Pix 15.14 0.3736 0.4165 28.3412 0.0053 0.1794 0.3217 0.4537 Pix2PixHD 17.27 0.5034 0.6688 21.2485 0.0032 0.1164 0.5168 0.6241 Pix2PixHD w/ ours 18.45 0.5377 0.7028 16.0702 0.0005 0.1123 0.6414 0.7730 TABLE I: Robustness comparison on the self-HER2 and MIST-Ki67 test sets under staining variations and acquisition degradations. Staining Variation Acquisition Degradation PSNR↑ SSIM↑ FID↓ KID↓ DISTS↓ DAB-KL↓ IOD-D↓ PSNR↑ SSIM↑ FID↓ KID↓ DISTS↓ DAB-KL↓ IOD-D↓ Self-HER2 ASP 15.52 0.2107 117.8376 0.0998 0.2939 0.7326 0.0361 16.2876 0.2389 157.5783 0.1403 0.2842 0.5559 0.0267 PyramidPix2Pix 17.39 0.3127 107.6362 0.0918 0.2868 0.4717 0.0270 17.9899 0.3321 93.2739 0.0722 0.2815 0.4064 0.0247 TDKStain 17.42 0.2860 80.3787 0.0440 0.2894 0.5423 0.0246 17.8115 0.3214 64.7279 0.0305 0.2808 0.3896 0.0258 UNIStainNet 17.37 0.2317 68.8050 0.0366 0.3211 0.4289 0.0252 17.0465 0.2524 63.4894 0.0316 0.3355 0.4165 0.0271 Pix2Pix 17.65 0.3254 78.6544 0.0519 0.2758 0.4154 0.0251 17.2000 0.3453 97.7118 0.0466 0.2541 0.4185 0.0245 Pix2PixHD 18.17 0.3114 88.4236 0.0652 0.2791 0.4667 0.0252 18.3600 0.3499 86.3794 0.0586 0.2661 0.4866 0.0253 Pix2PixHD w/ ours 18.40 0.3403 59.1927 0.0264 0.2613 0.3896 0.0249 18.4700 0.3619 59.5548 0.0283 0.2494 0.3821 0.0243 MIST-Ki67 ASP 14.23 0.2186 59.1870 0.0357 0.2608 0.6544 0.0391 14.5465 0.2330 59.8069 0.0349 0.2525 0.5929 0.0377 PyramidPix2Pix 13.97 0.2182 92.3648 0.0834 0.2644 0.5274 0.0378 14.3174 0.2321 90.5449 0.0757 0.2658 0.5181 0.0338 TDKStain 13.75 0.2127 61.2593 0.0423 0.2520 0.5811 0.0445 14.3700 0.2344 54.7415 0.0319 0.2383 0.5198 0.0321 UNIStainNet 14.46 0.1841 65.4040 0.0439 0.3041 0.5586 0.0390 14.2200 0.1890 62.9493 0.0337 0.3148 0.5531 0.0349 Pix2Pix 13.38 0.2357 85.2704 0.0546 0.2719 0.5852 0.0466 13.9137 0.2471 72.9535 0.0436 0.2689 0.5078 0.0428 Pix2PixHD 13.95 0.2266 123.0893 0.1070 0.2883 0.6755 0.0402 14.1927 0.2355 115.1264 0.0933 0.2860 0.5917 0.0379 Pix2PixHD w/ ours 14.74 0.2610 56.5030 0.0347 0.2599 0.5198 0.0345 14.8844 0.2737 49.2880 0.0289 0.2537 0.4907 0.0311 TABLE IV: Robustness comparison on the self-FFPE test set under staining variations and acquisition degradations. Staining Variation Acquisition Degradation PSNR↑ SSIM↑ FID↓ KID↓ DISTS↓ H-Dice↑ E-Dice↑ PSNR↑ SSIM↑ FID↓ KID↓ DISTS↓ H-Dice↑ E-Dice↑ Self-FFPE2HE ASP 15.52 0.3474 96.9358 0.0609 0.2879 0.2171 0.7507 15.5092 0.3455 99.5627 0.0595 0.2908 0.1746 0.7175 PyramidPix2Pix 17.12 0.4679 27.8536 0.0067 0.1529 0.5189 0.6592 16.8787 0.4581 27.6058 0.0055 0.1574 0.4951 0.6220 UNIStainNet 17.67 0.5151 21.2922 0.0025 0.2289 0.5735 0.7270 17.4587 0.4926 22.1434 0.0023 0.2429 0.5632 0.7253 Pix2Pix 13.75 0.3101 78.6262 0.0333 0.3039 0.2286 0.3185 14.7938 0.3512 32.0556 0.0058 0.1953 0.2956 0.4517 Pix2PixHD 16.91 0.4900 23.8326 0.0045 0.1251 0.4876 0.6065 16.4963 0.4664 24.1984 0.0043 0.1312 0.4623 0.5605 Pix2PixHD w/ ours 17.99 0.5191 18.1853 0.0013 0.1182 0.6112 0.7696 17.6075 0.4982 20.5926 0.0016 0.1230 0.6004 0.7400 Fig. 4: Four-class HER2 scoring performance using generated IHC images. Original H&E images and real IHC images are included as lower- and upper-reference inputs, respectively. TABLE V: Ablation study of Hessian-derived morphology preservation and histopathological realism constraints on the self-HER2 dataset. Method PSNR↑ SSIM↑ FID↓ DISTS↓ Supervised baseline 18.38 0.3321 87.6770 0.2807 Semi-supervised baseline 11.90 0.2048 455.7836 0.4586 Semi-supervised + HDMP 18.37 0.3428 73.6938 0.3001 Semi-supervised + HRC 18.42 0.3688 64.5625 0.2433 Ours 18.60 0.3704 52.4523 0.2335 IV-F Ablation Study We conduct ablation experiments to evaluate the individual and combined effects of HDMP and HRC. As reported in Table V, directly introducing unpaired source images without either constraint substantially degrades performance, demonstrating that unpaired optimization requires appropriate supervision. Adding HDMP or HRC individually substantially improves the semi-supervised baseline, while their combination achieves the strongest overall performance. HDMP transfers morphology-related supervision from the source image, whereas HRC promotes plausible target-stain characteristics. Their complementary effects support stable learning from unpaired source images. Fig. 5: Examples of input variations used for robustness evaluation. Each row begins with the original image, followed by three modified variants. The top and bottom rows illustrate staining variations and acquisition degradations, respectively. Fig. 6: Average PCC between generated images and their corresponding source images on the MIST-Ki67 and self-FFPE datasets. Higher values indicate stronger preservation of source-tissue organization. Fig. 7: Representative qualitative results on the three virtual staining tasks. The first two rows show FFPE-to-H&E translation, while the third and fourth rows show H&E-to-IHC virtual staining for HER2 and Ki67, respectively. Fig. 8: Sensitivity to the amount of unpaired source data. The unpaired-to-paired ratio is varied from 0.5:10.5:1 to 3:13:1 on the self-HER2, MIST-Ki67, and self-FFPE datasets. IV-G Robustness to Staining and Acquisition Variations The proposed framework emphasizes diagnostically relevant staining characteristics and tissue morphology, which should be less sensitive than superficial image appearance to incidental variations in staining and image acquisition. We therefore evaluate whether the learned translation remains stable when such variations are introduced while the underlying pathological content is preserved. Two modified versions of each test set are constructed to simulate staining variations and acquisition degradations, with representative examples shown in Fig. 5. Staining variations are generated by adjusting the hue, saturation, and brightness of the source images. Acquisition degradations are simulated using Gaussian noise, downsampling followed by Gaussian blur, and radial geometric distortion. The noise standard deviation is set to 2, the downsampling factor and blur-kernel size are set to 0.5 and 3, respectively, and the distortion coefficient is sampled from (−0.05, 0.05)(-0.05,\,0.05). Each operation is independently applied with a probability of 0.5. As presented in Tables I and IV, the proposed framework consistently improves Pix2PixHD under both types of input variation and achieves strong overall performance across image-level, distributional, and stain-specific evaluations. These results suggest that morphology preservation and histopathological realism constraints encourage the model to rely more on pathology-relevant staining and structural information, thereby reducing its sensitivity to incidental appearance and acquisition changes. IV-H Morphology Preservation Evaluation To evaluate whether virtual staining alters the spatial organization of the source tissue, we compute the Pearson correlation coefficient (PCC) between each generated image and its corresponding source image after grayscale conversion. For H&E-to-IHC translation, PCC is calculated between the generated IHC image and the input H&E image. For FFPE-to-H&E translation, it is calculated between the generated H&E image and the corresponding FFPE input. Grayscale conversion reduces the direct influence of stain color, while PCC measures the agreement between the spatial intensity patterns of the two images. A higher value indicates that the generated image retains more of the structural organization present in the source image. As shown in Fig. 6, the proposed framework achieves the highest PCC on both datasets, indicating stronger preservation of source-tissue organization. This result is consistent with the role of HDMP in reducing changes to tissue interfaces and cellular structures during stain translation. IV-I Sensitivity to the Amount of Unpaired Data We study the influence of unpaired data volume by setting the unpaired-to-paired ratio to 0.5:1, 1:1, 2:1, and 3:1, while keeping the remaining settings unchanged. As shown in Fig. 8, performance generally improves as additional unpaired source images are introduced and becomes relatively stable at a ratio of approximately 2:1. Increasing the ratio beyond this point provides limited additional benefit. We therefore use an unpaired-to-paired ratio of 2:1 in the remaining experiments. V Conclusion In this paper, we presented a stable semi-supervised framework for virtual staining that reduces reliance on accurately registered source–target pairs by jointly exploiting limited paired data and abundant unpaired source images. Hessian-derived morphology preservation extracts structural supervision from source images to preserve morphology-related spatial structures, while histopathological realism constraints guide generated images toward plausible target-stain characteristics. Together, they mitigate structural and appearance drift during semi-supervised optimization. Experiments on H&E-to-IHC for HER2 and Ki67, and FFPE-to-H&E translation demonstrate consistent improvements in image quality, morphology preservation, pathology-informed metrics, robustness, and downstream diagnostic performance. The robustness and ablation results further support the stability and complementary roles of the two proposed constraints. Overall, the proposed framework provides a practical approach for incorporating unpaired source images into virtual staining without modifying the underlying generator architecture. 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