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

Lalit Kumar

arXiv:2608.17370v1cs.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.

    Source: §1 · p. 1, §7 · p. 5

  • Method

    The authors train OT-coupled rectified flows between healthy and diseased clinical distributions and derive counterfactuals, risk scores, and attributions.

    Source: §1 · p. 1, §3 · p. 2

  • Results

    The central result is a synthetic-to-real gap: label-free heatmaps localize synthetic lesions but fail to transfer to real pathology.

    Source: §1 · p. 1

  • Takeaways & Limitations

    Compelling localization on planted lesions is not evidence that label-free heatmaps localize real disease.

    Source: §1 · p. 1

    The study is small, uses low-resolution imaging and a modest RSNA subset, and is not a clinical validation.

    Source: §8 · p. 7

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.Source: §1 · p. 1

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.Source: §1 · p. 1

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.Source: §1 · p. 1

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.Source: §1 · p. 1

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.Source: §1 · p. 1

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.Source: §2 · p. 2

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.Source: §2 · p. 2

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.Source: §2 · p. 2

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.Source: §2 · p. 2

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.Source: §2 · p. 2

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.Source: §3 · p. 2
  • 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.Source: §3 · p. 2

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.Source: §3 · p. 2
  • Optimal-transport endpoint pairings make rectified-flow target velocities low-variance and learned trajectories nearly straight.These properties support coarse Euler integration.Source: §3 · p. 2

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.Source: §4 · p. 2

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.Source: §4 · p. 2

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.Source: §4 · pp. 2–3

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.Source: §4 · p. 3

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.Source: §4 · pp. 2–3

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.Source: §5 · pp. 3–4

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.Source: §5 · pp. 4–5

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.Source: §5 · p. 4

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.Source: §5 · p. 4

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.Source: Figure 6 · p. 5

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.Source: Figure 7 · p. 5, §6 · p. 5

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.Source: §6 · p. 5

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.Source: §6 · p. 5

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.Source: §6 · p. 5

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.Source: §6 · p. 5, Figure 7 · p. 5

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.Source: §7 · p. 5

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).Source: §7 · p. 5, Table 5 · p. 6, Figure 8 · p. 6

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.Source: §7 · p. 6, Table 6 · p. 6, Figure 10 · p. 6

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.Source: Figure 9 · p. 6

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.Source: §7 · p. 6

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.Source: §8 · p. 7

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.Source: §8 · p. 7
  • 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.Source: §8 · p. 7

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.Source: §8 · p. 7
  • 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.Source: §8 · p. 7

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.Source: §9 · p. 7

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.Source: §9 · p. 7

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.Source: §9 · p. 7

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