Seeing Beyond the Lesion: Disease Recognition from Reactive CNS Tissue

Sampling error yields exclusively reactive, non-lesional brain parenchyma in a significant proportion of intracranial biopsies, leaving the underlying disease undiagnosed. We benchmark four pathology foundation models (UNI2-h, Virchow2, Prov-GigaPath, H-optimus-0) as frozen patch encoders within a shared attention-based multiple-instance learning framework using 245 whole-slide images from 186 patients with confirmed downstream diagnoses. We first show that coarse disease-category prediction can be reproduced largely from slide size alone. After restricting classification to three finer diagnostic distinctions within common tissue categories, this confound no longer explains performance, yet disease labels remain predictable above chance under permutation testing (p $\le 10^{-4}$ throughout). Surprisingly, performance is statistically indistinguishable across all foundation-model encoders, suggesting that recovering these weak morphological signatures is not limited by current patch representations. Signed instance-contribution maps and expert review further test whether predictive evidence localizes to reactive parenchyma rather than sampling-induced bias like blood introduced during tissue sampling. These results position acquisition-shortcut auditing via a provenance-only baseline as a necessary control in computational-pathology benchmarks, and show, once that confound is removed, that weakly supervised models still recover disease signal from tissue conventionally regarded as non-diagnostic.

Progressive Pseudo-Label Optimization for Point-Supervised Change Detection

Point-supervised change detection (PS-CD) aims to identify pixel-level changes between bi-temporal images using only sparsely annotated points. Although point annotations substantially reduce labeling costs, their limited spatial coverage often results in incomplete and noisy pseudo-labels. To address this issue, we propose a two-stage framework that introduces SAM2 priors into PS-CD and progressively adapts them to the target task. In Stage I, SAM2 generates object-aware candidate masks from point annotations on the bi-temporal images, and a bi-temporal mask selection strategy is designed to convert generic segmentation responses into more reliable change pseudo-labels. Subsequently, a lightweight CNN refinement module with an uncertainty-aware loss is employed to improve boundary quality and local structural consistency. In Stage II, we construct a teacher-student self-training framework in which the teacher is updated by exponential moving average and periodically refreshes the pseudo-labels. This design establishes a closed-loop optimization process that alternates between pseudo-label refinement and model re-optimization. Experiments on three benchmark datasets, including WHU-CD, LEVIR-CD, and SYSU-CD, demonstrate that the proposed method outperforms previous weakly supervised approaches on most benchmarks and remains competitive with several fully supervised methods.

CDGP: Contrastive Dual Gaussian Processes for Weakly Supervised Anomaly Segmentation

Industrial visual inspection must both decide whether a product is defective and localize the defect, yet pixel-level masks are costly to collect at scale. Most anomaly-segmentation methods learn only from defect-free images and score deviations from normality. A true defect and an unusual-but-normal region, however, can both deviate substantially and receive similarly high scores. We propose Contrastive Dual Gaussian Processes (CDGP), a weakly supervised framework that models normal and anomaly inducing-variable predictive distributions over dense tokens. Its posterior-dominance statistic standardizes their predictive-mean difference by the joint predictive uncertainty, providing both spatial evidence and image-level confidence. This evidence complements hierarchical normal-reconstruction residuals for fine localization. All calibration uses training data only, without human pixel annotations or test-time fitting. Across MVTec AD~2, KSDD2, and VisA, CDGP ranks first among the evaluated methods on all MVTec AD~2 localization metrics and is first-place or competitive on KSDD2 and VisA. Factorized and matched linear-head controls delimit the contribution and scope of the linear-kernel Gaussian process (GP) formulation.

Representation Is Not Enough: Body-Localized Thermal Evidence for Contactless Stress and Craving Sensing in Opioid Use Disorder

Removing wearables from physiological monitoring also removes their supervision: the signal indicating where and when a stress response occurred. Contactless stress sensing therefore becomes a weakly supervised evidence-localization problem, where a clip-level label must be traced to the body regions and moments that produced it. We address this with FABLE-Therm, a weakly supervised architecture that preserves localized evidence across body regions, time, and encoder-specific representations until the final decision. FABLE-Therm fuses frozen foundation-model encoders at the embedding level, with theory explaining why localized fusion can outperform feature concatenation and prediction averaging. We study this problem in opioid use disorder (OUD), where stress is a major relapse trigger and sustained wearable use can be difficult during early recovery. Using fixed thermal video, FABLE-Therm achieves 0.938 AUROC on held-out participants, and its learned representation transfers to self-reported craving, providing, to our knowledge, the first evidence that craving can be recovered from contactless thermal video. Localized evidence also enables participant-level analysis of deployment failure. We find that improving representation alone is insufficient for equitable deployment: additional data from the underserved group would recover only about half of the cohort gap, while the remainder reflects person-to-person heterogeneity. This modality-agnostic decomposition applies to models with identifiable subpopulations. Together with the first cohort-structured contactless thermal OUD benchmark, our results show that preserving localized evidence supports both accurate sensing and principled analysis of who a model fails and why.

LightTeaNet: A Weakly Supervised Lightweight CNN for Multi-Label Tea Leaf Disease Detection and Localization

Tea is known as an important crop in many parts of South and Southeast Asia, yet the production of tea is still hampered by the multiple diseases that decrease the quantity and quality. Traditional methods of inspection, which are manual, are not consistent, labor-intensive, and depend on extensive monitoring. This paper introduces a lightweight convolutional neural network (CNN) designed for weakly supervised multi-label classification and disease localization in tea leaves called LightTeaNet. LightTeaNet learns directly from image-level labels and employs Class Activation Mapping (CAM) to localize disease-affected regions automatically, unlike conventional object detection models such as YOLO, which require extensive bounding box annotations. For Parameter efficiency, the network integrates Depthwise Separable Convolutions, and for enhanced feature discrimination, it integrates Channel Attention. LightTeaNet has achieved a Precision of 0.9615, a Recall of 0.8772, and an F1-score of 0.9179, while it shows mAP@0.50=0.1810 without any manual annotations, which delivers a competitive localization performance in the experimental results. These results validate the model as an interpretable as well as a resource-efficient framework for intelligent disease monitoring in agriculture.

Localizing to Debias: A Patch-Level Benchmark and Baseline for Weakly Supervised Spatial Anomaly Detection

Despite growing interest in weakly supervised video anomaly detection (WSVAD), current methods struggle to bridge the gap between coarse temporal supervision and fine-grained spatial reasoning. A key obstacle is the tendency of temporal detectors to latch onto background and scene-level cues rather than truly discriminative anomaly evidence. This background bias raises ethical concerns: models may inadvertently associate anomalies with societal or environmental context rather than authentic crime-related cues. Without spatial grounding, such biases remain hidden and unauditable. To address this, we propose SST-WSVADL, a sparse spatio-temporal framework that bridges temporal anomaly detection with fine-grained spatial localization. Rather than processing all spatial regions indiscriminately, SST-WSVADL progressively focuses on the most anomaly-relevant spatio-temporal regions through dynamic sparsification, naturally suppressing background dominant content while preserving discriminative evidence. The temporal and spatial branches are coupled end-to-end via motion-aware regularization that guides sparsification toward dynamically informative regions, without relying on external detectors or vision-language prompts. We publicly release frame-level spatial annotations and a method-agnostic evaluation protocol for three public datasets: UCF-Crime, XD-Violence, and MSAD. These resources enable the community to audit spatial biases in WSVAD predictions, supporting progress toward more ethical and accountable anomaly detection. Experiments demonstrate that SST-WSVADL is competitive with prior methods across benchmarks while enabling localization and patch-level auditability of scene bias, providing a reproducible foundation for interpretability-oriented evaluation of WSVAD models.

DeCo-MIL: Debiased Counterfactual Reasoning for Long-Tailed Whole Slide Image Analysis

Multiple instance learning (MIL) is widely used for weakly supervised whole slide image (WSI) analysis. However, under long-tailed distributions, MIL-based WSI analysis faces a nested dual long-tail: an inter-slide class long tail and an intra-slide long tail of instance-level discriminative evidence. The two long tails are coupled: tail classes have few training slides, while their limited diagnostic evidence is concentrated in a few patches and obscured by abundant within-bag redundancy. This coupling biases models toward head classes and degrades rare-class recognition. To address this, we propose DeCo-MIL for long-tailed WSI analysis, which jointly alleviates the nested dual long-tail through frequency-debiased counterfactual reasoning. For the inner long tail, DeCo-MIL clusters patches into tissue-morphology anchors, replaces each anchor with its matched normal prototype to perform a counterfactual intervention, and estimates its counterfactual contribution to the ground-truth class using class-frequency-corrected predictions. These contributions guide redundancy masking to preserve scarce discriminative instances. For the outer long tail, DeCo-MIL constructs anchor-stratified pseudo-bags from redundancy-reduced bags and combines tail-aware oversampling with consistency regularization, increasing effective supervision for tail classes while preserving tissue-morphology composition. Extensive experiments on three long-tailed WSI benchmarks demonstrate that DeCo-MIL achieves state-of-the-art performance in both tail-class recognition and overall classification.

MuST-VAD: Mutual Structured Learning for Video Anomaly Detection

In this paper, we propose MuST-VAD, a mutual structured learning framework for weakly supervised video anomaly detection (VAD) in which an anomaly detector and a large vision-language model (LVLM) exchange their acquired knowledge. Detectors in weakly supervised VAD learn anomaly scores from features extracted by a fixed, task-agnostic backbone. These fixed features bound the achievable detection accuracy. Recent methods therefore transfer LVLM semantics into the detector as richer features. However, this transfer is one-way: what the detector learns about the target videos never returns to the LVLM. MuST-VAD extends the one-way transfer into a bidirectional learning loop. In this loop, the latest detector predictions supervise the LVLM adaptation, and the adapted LVLM returns updated representations that retrain the detector; the two models alternate these updates over small video groups. Both models train on detector-selected key clips, while confidence weighting and annotation-anchored question answering keep the exchanged supervision reliable. On UCF-Crime, our mutual learning improves the one-pass transfer baseline from 88.15% to 88.63% AUROC and from 37.25% to 42.46% average precision (AP), outperforming the state-of-the-art method in AP by 4.13 points.

Recent advances in weakly supervised learning: New supervision paradigms, assumption relaxations, and practical solutions

Deep learning has achieved great success in recent years thanks to the availability of high-quality, well-annotated training data. However, this requirement is often not met in real-world applications. Weakly supervised learning aims to train an accurate model with incomplete, inexact, or inaccurate supervision. In this chapter, we will discuss recent advances in this field, including new supervision paradigms, relaxed assumptions, and practical solutions. First, we introduce a new weakly supervised binary classification problem called confidence-difference classification and propose consistent approaches to solve it. Next, we investigate complementary-label learning, a weakly supervised multi-class classification problem. Our proposed approaches are based on more relaxed assumptions about the data generation process than existing consistent approaches. Lastly, we present an evaluation framework for partial-label learning, another popular multi-class weakly supervised learning problem, in order to promote fair and realistic evaluation of algorithms in this field.

Bag-of-Visual-Words for Spatial Mapping of Lung Adenocarcinoma Growth Patterns

Spatial mapping of lung adenocarcinoma (LUAD) growth patterns across whole slide images (WSIs) requires resolving architectural context at the region level, yet existing methods operate at the individual tile level and produce generic morphological clusters rather than clinically defined pattern maps. We propose a weakly supervised Bag-of-Visual-Words (BoVW) pipeline that learns a visual vocabulary from frozen foundation model embeddings extracted from a small set of annotated regions of interest (ROIs). Pattern prototypes are constructed as mean BoVW histograms of same-label ROIs and used for nearest-prototype classification of sliding-window regions under Jensen--Shannon divergence. The resulting predictions are projected onto the WSI tile grid to produce interpretable spatial pattern maps. We evaluate the method on 87 CPTAC-LUAD patients using three foundation model encoders and multiple vocabulary sizes on two clinically motivated tasks. For tumour/healthy classification, the best configuration achieves a balanced accuracy of $0.974$ with H-Optimus-1, approaching the $0.987$ obtained by a supervised SVM trained on mean-pooled WSI embeddings. For binary histologic grade classification, the BoVW pipeline achieves higher balanced accuracy than the supervised baseline for all encoders, suggesting that ROI-level pattern decomposition preserves grade-relevant heterogeneity that is attenuated by global mean pooling.

From Spatial Semantics to Temporal Context: Leveraging Gaze Trajectory for Weakly Supervised Medical Image Segmentation

Medical image segmentation heavily depends on labor-intensive and time-consuming pixel-level annotations. Eye tracking offers a cost-effective solution that can be naturally integrated into clinical workflows. Recorded by eye trackers, gaze conveys the spatial regions of clinicians' attention through fixations and the temporal context of clinicians' progressive visual perception from trajectories. Nevertheless, effective modeling of temporal trajectories remains challenging, and noise in gaze caused by exploratory fixations greatly limits segmentation performance. To overcome these limitations, we propose the Trajectory-guided Uncertainty-aware Network (TrailNet), which exploits gaze-supervised medical image segmentation from spatial semantics modeling to temporal context by jointly leveraging fixations and trajectories. Specifically, the proposed trajectory-guided spatio-temporal encoder models temporal context and establishes complementary interactions with image spatial semantics to strengthen target perception. Furthermore, the multi-scale uncertainty decoder leverages category mutual-exclusivity constraints to produce deterministic predictions and mitigate supervision uncertainty induced by noise. To enable gaze-free inference, we further introduce a cycle distillation strategy that transfers feature-level knowledge via teacher-student networks. Experimental results on two public datasets demonstrate that TrailNet outperforms state-of-the-art methods, achieving Dice scores of 81.25% and 81.85%, respectively.

A Diagnostic Gap Framework for Evaluating Reconstruction Fidelity in Weakly Supervised Mammography

Weakly supervised pipelines for medical imaging have become increasingly popular over the years. These systems often include multiple stages and components, such as reconstruction, generation, and localization, yet standard evaluation metrics provide limited insight into whether clinically relevant information is preserved across each stage. We present the diagnostic gap framework, a practical evaluation tool that measures decision preservation and explanation preservation as a function of measured reconstruction fidelity. To isolate the effect of reconstruction from localization, we evaluate on curated lesion ROI crops using a fidelity ladder of three class-conditional reconstructors---VQ-VAE-GAN, VAE-GAN, and diffusion (SDEdit)---spanning a twenty-fold range in perceptual distance (LPIPS 0.029--0.584). At autoencoder fidelity, both decision and explanation are preserved: AUC changes remain within $\pm$0.005 and attribution similarity (HiResCAM, Grad-CAM++) stays high. At diffusion fidelity, both collapse: pooled AUC drops by 0.253 and mass-pathology AUC falls below chance. The diagnostic gap is thus a measurable function of reconstruction fidelity rather than an intrinsic cost of reconstruction, and the framework provides an architecture-agnostic instrument for identifying when and where multi-stage pipelines lose diagnostic signal.

Weakly Supervised Pathology-Informed Representation Learning for PET-Based Content Retrieval of Intra-Tumour Heterogeneity

We propose a weakly supervised 18FFDG PET representation-learning framework for content based medical image retrieval, using H&E derived information during training while preserving PET-only inference. The proposed method was designed to use H&E derived information during training while maintaining PET only inference. A teacher student training strategy was used to learn the PET tumour derived voxel representations, from which global and hotspot conditioned embeddings were generated along with maps of intra tumour heterogeneity in our oesophegeal cancer test case. A progressive ablation strategy was used to evaluate the contribution of different supervision mechanisms. Retrieval performance was assessed across cross-validation folds using metrics including mean average precision, normalised discounted cumulative gain and mean reciprocal rank. Additional analyses evaluated ablation performance, hotspot faithfulness through perturbation/deletion experiments, prototype-specific PET uptake behaviour and indirect patient level concordance between learned PET prototype classes and selected histomic features. Progressive introduction of pathology informed supervision and hotspot modelling improved PET retrieval performance compared with global PET representations and conventional PET baselines. Across the ablation ladder, PET hotspot conditioned representations consistently provided stronger retrieval than global embeddings, indicating that focusing on informative tumour subregions improved sensitivity to intra tumour heterogeneity. Histopathology concordance further showed that the learned classes were not simply high uptake PET regions; instead, they demonstrated distinct heterogeneity in 18F FDG uptake.

AnomExpert: Identifying and Selecting Anatomical Planes for Prenatal Ultrasound Anomaly Diagnosis

Life-limiting congenital anomalies require accurate prenatal diagnosis for appropriate clinical decision-making. Prenatal ultrasound (US) examinations involve multiple anatomical planes, and diagnosis depends on identifying anatomical planes and selecting diagnostically relevant planes for each anomaly. Existing automated methods either rely on plane-level annotations or aggregate heterogeneous images without explicitly modeling these diagnostic capabilities. We propose AnomExpert, a prototype-driven framework for prenatal US anomaly diagnosis using only case-level supervision. AnomExpert introduces learnable plane prototypes to organize unordered images into latent representations corresponding to anatomical planes without requiring plane annotations. A disease-aware sparse selection mechanism further selects diagnostically relevant planes for each anomaly. Experiments on a multi-center dataset of 3,654 cases show that AnomExpert consistently outperforms nine representative multi-instance learning methods. Using a ViT-small backbone, it achieves 86.9% accuracy and 84.2% F1-score while maintaining parameter efficiency. These findings indicate that modeling anatomical plane identification and disease-specific plane selection improves weakly supervised multi-plane prenatal US anomaly classification. The code is available at https://github.com/TIanCat/AnomExpert.

Weakly Supervised Spatio-Temporal Candidate Discovery of Dairy Farm Sites from Seasonal Satellite Imagery

Farm site discovery from satellite imagery is a spatiotemporal candidate ranking problem because farm evidence is distributed across pasture, field boundaries, roads, buildings, and seasonal vegetation patterns. Direct farm labels are often incomplete, which makes fully supervised detection difficult. This paper proposes a weakly supervised pipeline for ranking dairy farm candidate clusters from seasonal Sentinel imagery and open map priors. The method uses aligned spring, summer, and autumn image tiles from County Cork, Ireland, with spectral bands, vegetation indices, built area indices, and a pasture channel. A Barlow Twins encoder learns multi-season tile embeddings without farm labels. In parallel, weak OpenStreetMap farm priors are split into a prior and a held-out set. Prior features support a rule-based tile score that combines farm proximity, seasonal pasture evidence, and summer greenness, while held-out features are reserved only for proxy evaluation. The rule score is smoothed over a spatial representation graph using geographic proximity and embedding similarity, and high-scoring tiles are grouped into ranked candidate clusters. From 26,722 valid tiles, the main run selects 535 high-confidence tiles and forms 71 candidate clusters. The top 5 clusters achieve 0.60 precision within 500 m and 0.80 precision within 1000 m of held-out OpenStreetMap farm features. The top 10 clusters achieve 0.40 precision within 500 m and 0.80 precision within 1000 m. The results show that seasonal representation learning and weak geographic priors can reduce large satellite image collections into compact candidate sets for human review.

CGRL: Concept-Guided Pruning and Representation Learning for Whole-Slide Image Classification

Weakly supervised whole-slide image (WSI) classification is widely used in computational pathology because slide-level labels are easier to obtain than dense region annotations. Existing multiple instance learning (MIL) methods often aggregate large bags of patch embeddings using mainly visual cues, which can retain many non-informative patches and provide weak alignment between instance features and class-level disease semantics. We propose Concept-Guided Pruning and Representation Learning (CGRL), a simple framework that introduces class-level concept prototypes derived from disease prompts into the MIL pipeline. First, concept-relevance pruning ranks patch instances by their similarity to class concepts and retains the top-K concept-relevant patches for downstream MIL aggregation. Second, concept-guided contrastive representation learning constructs class-wise positive and negative patch sets from the same similarity matrix and optimizes target-class, symmetric auxiliary, and cross-class separation objectives, thereby regularizing the projected concept space. We evaluate CGRL on TCGA-BRCA and TCGA-NSCLC using multiple representative MIL methods. Experimental results show that CGRL improves several model-dataset combinations, with gains depending on the downstream MIL model and dataset. It achieves particularly clear improvements in accuracy and macro-F1 while reducing computational cost through concept-relevance pruning. These findings demonstrate that class-level semantic concepts provide an effective and practical prior for patch selection and representation learning in weakly supervised computational pathology.

Learning to Distort: Weakly-Supervised Image Quality Transfer for Prostate DWI Correction

Single-shot echo-planar prostate diffusion-weighted imaging (DWI) is frequently complicated by geometric distortions, which impact the ability to derive reliable diagnoses from such images. Developing automated correction methods is challenged by the absence of paired distorted and undistorted clinical scans. In this paper, we first propose a novel weakly-supervised image quality transfer (IQT) framework from undistorted to distorted images that utilizes image quality assessment (IQA) signals to supervise the transfer process. Unlike traditional methods that require expensive, voxel-wise paired data or resort to developing unpaired algorithms, our approach utilizes image-level quality labels (here, distorted vs. undistorted) to establish latent quality prototypes within a pre-trained feature space. Recognizing that simulating realistic distortions is more reliable than direct unpaired correction, we describe a weakly-supervised prototype flow matching algorithm to explicitly regularize generative trajectories towards distorted prototypes, producing realistic susceptibility artifacts that mimic clinical degradations. By synthesizing these realistic pairs, we enable a second IQT model to be trained in the forward direction for distortion correction. Experimental results demonstrate that our generated images successfully mimic the diagnostic interference of real-world artifacts, which leads to more capable distortion correction IQT models. In addition to qualitative comparisons, we also conduct exhaustive quantitative evaluations that compare our approach with existing unpaired approaches (e.g., CycleGAN, UNIT-DDPM, and OT-FM) - as either forward or reverse alternatives - by assessing clinical downstream task performance in PI-RADS and Gleason score classification, using both in-distribution and external data sets.

Overhead Wildlife Locator (OWL): Benchmarking Weakly Supervised Learning for Aerial Wildlife Surveys

Automated aerial wildlife surveys increasingly rely on deep learning, yet standard object detectors require bounding-box annotations, reported to be up to seven times slower and three times more expensive to produce than point-level labels. To address this bottleneck, we introduce the Overhead Wildlife Locator (OWL), a weakly supervised density-estimation framework with three variants: OWL-C, a fully convolutional model for high-throughput screening; OWL-T, a Swin-augmented hybrid for heterogeneous, cluttered scenes; and OWL-D, built on a frozen DINOv3 ViT-H+/16 encoder with a DPT-style fusion decoder. We benchmark all three against POLO, YOLOv11n, and YOLOv11l across five public aerial datasets, from sparse fixed-wing savanna surveys to dense UAV paddock imagery, and against the published HerdNet baseline on its native Delplanque split. OWL-D sets a new state of the art on Delplanque (0.934 AP vs. HerdNet's 0.840) and records the highest AP on four of the five datasets. Performance is regime-dependent: on the extreme-density SheepCounter UAV dataset the hybrid OWL-T leads (0.978 AP) and the convolutional variants attain the lowest counting error, whereas the foundation-based OWL-D degrades, indicating which variant suits which survey type. We further validate operational readiness on the Alaska Department of Fish and Game's 2022 Central Arctic Caribou census: under cross-herd and cross-temporal transfer, OWL-C fine-tuned on the 2017 Porcupine Caribou Herd split attains F1 = 0.965 on a held-out patch test set, with a signed count error of +3.1% aggregated across the released test patches. We release the OWL code, model weights, and the annotated Porcupine Caribou Herd 2017 (PCH) and Central Arctic Herd 2022 (CAH) patches, the first open patch-level datasets for large-scale caribou aerial surveys, at https://github.com/microsoft/MegaDetector-Overhead.

AGE-MIL: Anchor-Guided Evidence Learning for Patient-Level Prediction

Existing computational pathology methods predominantly operate within whole-slide image (WSI)-level multiple instance learning (MIL) paradigms, while patient-level modeling remains underexplored. In routine pathological practice, however, pathologists derive diagnostic and prognostic conclusions by integrating evidence across multiple WSIs rather than relying on any single slide. This discrepancy creates a fundamental misalignment when patient-level supervision is directly imposed on conventional MIL frameworks, often leading to unstable optimization and degraded predictive reliability. To address this issue, we propose Anchor-Guided Evidence MIL (AGE-MIL), a weakly supervised framework for patient-level prediction. AGE-MIL constructs a patient-level anchor from slide representations to capture global pathological context and guide the retrieval and integration of diagnostically relevant local patches, enabling robust patient-level modeling. Patient-level risk is further modeled as an evidence accumulation process, promoting stable optimization under weak supervision. AGE-MIL is evaluated on six clinically relevant patient-level prediction tasks from two independent cohorts. Experimental results show that the proposed framework consistently outperforms eight state-of-the-art MIL methods. Code is available at https://github.com/wodeniua/AGE-MIL.

Semantic Segmentation for Histopathology using Learned Regularization based on Global Proportions

In pathology, the spatial distribution and proportions of tissue types are key indicators of disease progression, and are more readily available than fine-grained annotations. However, these assessments are rarely mapped to pixel-wise segmentation. The task is fundamentally underdetermined, as many spatially distinct segmentations can satisfy the same global proportions in the absence of pixel-wise constraints. To address this, we introduce Variational Segmentation from Label Proportions (VSLP), a two-stage framework that infers dense segmentations from global label proportions, without any pixel-level annotations. This framework first leverages a pre-trained transformer model with test-time augmentation to produce a pixel-wise confidence estimate. In the second stage, these estimates are fused by solving a variational optimization problem that incorporates a Wasserstein data fidelity term alongside a learned regularizer. Unlike end-to-end networks, our variational method can visualize the fidelity-regularization energy, resulting in more interpretable segmentation. We validate our approach on two public datasets, achieving superior performance over existing weakly supervised and unsupervised methods. For one of these datasets, proportions have been estimated by an experienced pathologist to provide a realistic benchmark to the community. Furthermore, the method scales to an in-house dataset with noisy pathologist labels, severely outperforming state-of-the-art methods, thereby demonstrating practical applicability. The code and data will be made publicly available upon acceptance at https://github.com/xiaoliangpi/VSLP.