Pathology Transport: Optimal-Transport Explanations for Clinical Data, and When Their Heatmaps (Fail to) Localize Disease

Lalit Kumar

Source-linked AI summary

Pathology Transport: Optimal-Transport Explanations for Clinical Data, and When Their Heatmaps (Fail to) Localize Disease

Lalit Kumar

arXiv:2608.17370v1Aug 18, 2026cs.LG

TL;DR

The paper asks whether classifier-free optimal-transport explanations genuinely localize disease rather than merely appear plausible. It finds a synthetic-to-real gap: label-free heatmaps can localize planted lesions but fail to localize real pathology.

Problem
The paper investigates whether classifier-free generative explanation heatmaps genuinely localize pathology, a question rarely tested directly.
Method
The authors train OT-coupled rectified flows between healthy and diseased clinical distributions and derive counterfactuals, risk scores, and attributions.
Results
The central result is a synthetic-to-real gap: label-free heatmaps localize synthetic lesions but fail to transfer to real pathology.
Takeaways & Limitations
Compelling localization on planted lesions is not evidence that label-free heatmaps localize real disease.
Takeaways & Limitations
The study is small, uses low-resolution imaging and a modest RSNA subset, and is not a clinical validation.

Abstract

from arXiv · show

Generative models promise a route to explainable clinical AI: rather than probe a classifier, model the distributions of healthy and diseased patients and read explanations off the geometry between them. We build such a system - an optimal-transport rectified flow trained between two clinical distributions - and use it to ask a pointed question the field too rarely tests: do the resulting explanation heatmaps actually localize disease? On tabular tumour biomarkers (Breast Cancer Wisconsin) a single flow yields per-patient counterfactuals, an unsupervised malignancy score (AUROC 0.91; 0.93 +/- 0.01 across five seeds), and a label-free attribution that agrees with a supervised classifier (r ~ 0.5) - a compact, honest interpretability engine, though it never out-predicts logistic regression. Moving to chest X-rays, we show the transport heatmap is a population-level signal, not a localiser; a reconstruction-based, identity-preserving variant does localize synthetic lesions (pointing game 0.52), yet on real RSNA radiologist boxes it collapses to chance while only supervised Grad-CAM stays above it. The central result is a synthetic-to-real gap: label-free heatmaps that look compelling on planted lesions are not evidence of real localisation. We contribute a reusable optimal-transport recipe for generative explanations and a controlled benchmark for stress-testing whether they localize.

1 Introduction

The paper proposes explaining clinical predictions by learning optimal-transport geometry directly between healthy and diseased populations, without training a classifier. A single transport model yields counterfactuals, an unsupervised risk score, and population attribution, while exposing limitations including off-manifold drift, non-sparse edits, and no accuracy gain over logistic regression.

Motivation and method: The method learns an optimal-transport map between benign and malignant patient distributions rather than perturbing inputs against a fixed classifier.OT-coupled rectified flow implements this distribution-level approach.
Interpretability engine: One transport model produces per-patient counterfactuals, an unsupervised risk score from travel length, and a global attribution from average displacement.These three interpretability artefacts are evaluated quantitatively on the Breast Cancer Wisconsin (Diagnostic) dataset.
Evaluation setting: 569 biopsies and 30 nuclear biomarkers make the Breast Cancer Wisconsin (Diagnostic) dataset a real, offline clinical test with a known biomarker signature.The dataset is used to test the proposed explanation engine.
Evaluation scope: The study explicitly tests whether generative heatmaps genuinely localize disease, rather than assuming visually compelling explanations are clinically actionable.This question motivates the imaging half of the paper.
Limitations: The approach has no accuracy gain over logistic regression, can make non-sparse edits, and may derive discrimination partly from off-manifold drift.The paper also warns that transport can fabricate off-manifold patients and that unsupervised scores need not match supervised classifiers.

2 Related Work

Prior work frames counterfactuals, clinical attribution, generative edits, and image saliency around classifier-based explanations or supervised localisation. This work instead uses an unconditional optimal-transport-coupled rectified flow to define counterfactual edits and label-free pathology explanations.

Counterfactual explanations: Counterfactual explanations seek nearest decision-flipping inputs, often augmented with validity, sparsity, and plausibility constraints.The proposed counterfactual comes from a generative transport map rather than gradient descent against a classifier, so it remains defined without a classifier and is biased toward the data manifold.
Explainable AI in healthcare: SHAP and related feature-attribution methods explain trained clinical predictors, but cannot synthesize an alternative-verdict patient or localize pathology without supervised detection.The transport-based view is presented as complementary because it explains disease-related distributional change rather than only a model decision.
Generative and diffusion counterfactuals: Generative medical counterfactuals, including diffusion methods, morph diseased scans toward healthy versions but still use external classifiers for guidance.This approach instead defines edits through transport between two unconditional class distributions.
Saliency, localisation, and faithfulness: Image explanation work evaluates supervised Grad-CAM and map quality with deletion/insertion faithfulness plus pointing-game/IoU against ground-truth boxes.The label-free localiser follows healthy-anatomy reconstruction methods such as f-AnoGAN and autoencoder anomaly segmentation, where reconstruction error flags abnormalities.
Flow matching and optimal transport: Rectified flow and flow matching regress velocities toward straight-line interpolations, while mini-batch optimal-transport pairing straightens trajectories and improves sample quality.This OT coupling is central to the method’s stability and motivates applying an OT-coupled rectified flow between clinical distributions.

3 Background

Optimal transport defines an economical transformation between source and target distributions by minimizing transport cost. Rectified flow represents this transport as an ODE learned from straight-line endpoint pairings, with optimal-transport pairings producing low-variance velocities and nearly straight trajectories.

Optimal transport: Optimal transport seeks a map or plan that morphs source distribution μ into target distribution ν at minimum total cost.Under squared-Euclidean cost, the Kantorovich relaxation optimizes over couplings between μ and ν.
Optimal transport: OT pairs each source point with the most cheaply reachable target point, yielding an economical and interpretable population transformation.The full continuous plan is approximated per minibatch with a discrete assignment.
Rectified flow: Rectified flow carries samples from μ at t=0 to ν at t=1 using an ordinary differential equation with learned velocity v_θ(x,t).It regresses velocity toward the straight-line direction between paired endpoints through flow matching rather than simulating a stochastic process.
Rectified flow: Optimal-transport endpoint pairings make rectified-flow target velocities low-variance and learned trajectories nearly straight.These properties support coarse Euler integration.

4 Methodology

The method trains an optimal-transport-coupled rectified flow from benign to malignant clinical distributions, using standardized biomarkers and paired endpoint interpolations. It produces risk scores, counterfactuals, and population-level attributions, with optimal-transport pairing substantially improving edit size and attribution coherence.

Data: The Breast Cancer Wisconsin dataset provides 569 biopsies described by 30 standardized nuclear biomarkers, with malignant cases as the positive class and 30% held out for evaluation.Standardization uses training-split statistics, making transport displacement comparable across biomarkers.
Rectified flow: A time-conditioned velocity field transports the benign distribution to the malignant distribution through an ODE trained on straight-line interpolations between paired endpoints.The velocity field is implemented as a four-layer SiLU multilayer perceptron with sinusoidal time embedding.
Three artefacts: The two directional flows yield a transport-magnitude risk score, benign-to-malignant counterfactuals whose displacement names biomarkers, and cohort-averaged population attribution.Flows are integrated with a 100-step Euler integrator under exponential-moving-average weights.
Baselines and metrics: Risk scores are evaluated by AUROC against supervised logistic regression and distance to the benign mean, while counterfactuals and attribution use validity, plausibility, individualisation, and logistic-regression comparisons.Counterfactuals are compared with a mean-shift baseline that adds the constant class-mean difference to every patient.
Optimal-transport coupling: Optimal-transport pairing shrinks the mean counterfactual edit from 25.3 to 9.6 and changes population attribution from anti-correlated noise (r = −0.03) to a clinically coherent signal (r = 0.49).Mini-batch assignments are solved with the Hungarian algorithm; independent random pairing otherwise produces high-variance targets and off-manifold integration.

5 Results

The transport flow provides unsupervised malignancy scoring, individualized counterfactuals, and label-free biomarker attributions, while remaining below supervised logistic regression on discrimination. Its learned trajectories are coherent, but its advantage is explanation generation rather than raw predictive performance.

Unsupervised risk score: 0.912 AUROC was obtained without labels during flow training, exceeding the naive baseline at 0.882 but not supervised logistic regression at 0.992.Part of the transport score’s discrimination reflects off-manifold drift rather than a calibrated likelihood.
Per-patient counterfactuals: 84% of flow counterfactuals were valid, with individualized edit directions whose cosine similarity was 0.64 versus 1.00 for mean-shift.The worked example increased concavity, concave points, perimeter, and area, while mean-shift flipped 100% of cases using a generic edit.
Population attribution: r=0.49 correlation with logistic-regression coefficients showed that label-free transport attributions recovered malignancy drivers including concavity, concave points, perimeter, radius, and area.The agreement was obtained by moving one distribution onto another without labels.
Unsupervised risk score: 0.934 ± 0.012 AUROC was achieved by the transport risk score across five splits, versus 0.894 ± 0.016 for the naive baseline and 0.992 ± 0.004 for logistic regression.The ranking and performance gaps remained stable across seeds.
Image risk score: 0.67 AUROC was achieved by the image transport score, above naive mean-intensity at 0.58 but below a supervised pixel classifier at 0.93.This reproduced the tabular pattern of unsupervised transport outperforming a naive baseline but not a supervised classifier.

6 Extension to Chest X-ray Images

The identical optimal-transport flow recipe extends to raw chest-X-ray pixels, enabling disease synthesis, risk scoring, and spatial attribution. However, its heatmaps are only qualitative visualisations: on planted lesions they barely exceed chance and trail supervised Grad-CAM, while the risk score is moderately discriminative.

Spatial attribution: For real pneumonia inputs, the reverse-flow difference concentrates in lung fields, but its faithfulness requires direct evaluation rather than visual inspection.The figure describes F_p→n(x) − x as the signal removed to normalise the lung.
Ground-truth localisation: 0.17 pointing-game accuracy: the population transport heatmap barely exceeds a random map and trails supervised Grad-CAM at 0.57 on inserted lesions.The controlled benchmark inserts a soft Gaussian opacity at a known location and evaluates pointing-game accuracy, IoU, and lesion-contained heatmap energy.
Method: OT-coupled rectified flows between normal and pneumonia chest X-rays replace the tabular MLP with a time-conditioned convolutional U-Net.The 28×28 PneumoniaMNIST setup trains separate normal→pneumonia and pneumonia→normal flows for synthesis, scoring, and localisation.
Risk score: 0.67 AUROC: edit-distance risk scoring exceeds mean intensity at 0.58 but trails supervised pixel-level logistic regression at 0.93.This reproduces the broader pattern that the transport score is informative but not competitive with supervised prediction.
Synthesis and spatial attribution: The flow synthesises plausible disease progression and produces lung-field attribution maps without pixel-level labels.At 28×28 resolution, the synthesised images are blurry and the attribution remains a qualitative visualisation rather than a validated detector.

7 Do Generative Heatmaps Localize Disease?

This section tests whether generative transport heatmaps localize pathology, first on controlled synthetic lesions and then on real radiologist-annotated chest X-rays. An identity-preserving normal-manifold autoencoder succeeds synthetically but fails to transfer to real lesions, exposing a synthetic-to-real localization gap.

Evaluation question: The section evaluates localization on synthetic lesions before testing transfer to real radiologist annotations.The benchmark proceeds from controlled synthetic lesions to real RSNA lesion boxes.
Synthetic lesions: The population transport map is near-random, while the normal-manifold autoencoder concentrates on synthetic lesions.The sparse counterfactual fails at 0.08 because the CNN only weakly flags the synthetic opacity (p=0.61).
Real pathology: On real RSNA lesion boxes, the label-free autoencoder is no better than random, while only supervised saliency exceeds chance.The real-data evaluation used 80 held-out positives, with higher localization scores indicating better performance.
Synthetic lesions: 0.52 pointing game and 0.36 IoU: the identity-preserving normal-manifold autoencoder tightly localizes synthetic lesions at 128×128.A simple supervised Grad-CAM does not localize focal opacities at this resolution.
Real pathology: Tripling healthy training data, denoising, and reconstruction-derived lung masking do not improve localization beyond random-map performance.These results indicate that tuning is insufficient and stronger anomaly models are needed.

8 Limitations

The study is a controlled, small-scope investigation rather than a clinical validation. Its datasets, image resolution, and modest classifier limit generalisability, and all artefacts tie or trail a simple supervised baseline.

Study scope: The study is a controlled investigation, not a clinical validation, with deliberately limited scope.The authors frame the contribution as characterisation rather than clinical deployment or validation.
Scale and cohorts: The tabular experiments use a single 569-patient cohort, limiting cohort diversity.No additional tabular cohorts are included in the stated study scope.
Scale and cohorts: The imaging experiments use 28–128 px inputs and an ∼1.4k-image RSNA subset, constraining imaging scale and resolution.These settings are substantially narrower than broad clinical imaging validation.
Baseline limitations: AUROC 0.68–0.75 for the imaging classifier means its Grad-CAM provides a floor, not a ceiling, for comparison.The classifier is described as modestly accurate, so supervised attribution performance may not represent the attainable upper bound.
Baseline limitations: Every artefact ties or trails a simple supervised baseline, so the contribution is honest characterisation rather than state-of-the-art performance.The paper does not claim a method win over the supervised baseline.

9 Conclusion

The paper reframes diagnosis as optimal transport between clinical distributions, yielding counterfactuals, an unsupervised malignancy score, and label-free biomarker attribution across modalities. It emphasizes that these outputs are explanatory aids requiring clinical caution, while outlining extensions toward actionable counterfactuals, calibrated risk, unified conditioning, and improved localization.

Contributions: OT-coupled rectified flows produced coherent per-patient counterfactuals, an unsupervised malignancy score (AUROC 0.91), and label-free biomarker attribution agreeing with a supervised classifier (𝑟=0.49).The same recipe also synthesized disease progression and produced a spatial pathology heatmap on chest X-rays.
Ethical and clinical considerations: The transport model should be treated as a hypothesis-generating explanatory aid, not a diagnostic device, because synthesized patients and lungs can mislead without context.The unsupervised score is uncalibrated and should never independently gate care; both datasets are small and demographically narrow.
Future work: Future extensions include sparse counterfactual penalties, exact flow log-likelihood for calibrated risk, a unified class- and time-conditioned field, and stronger anomaly models.The proposed anomaly-model directions include self-supervised and diffusion-based restoration approaches to close the synthetic-to-real localization gap.