cs.LGAug 18, 2026

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

Authors: Lalit Kumar

Organizations: Department of Computer Science The University of Texas at Austin

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Abstract

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.

Figures & tables

Figure 1. Workflow. Standardised biomarkers are split into benign (source) and malignant (target) sets. Within each mini-batch a Hungarian optimal-transport assignment pairs source and target points; a time-conditioned velocity field vθ(xt,t)v_{\theta}(x_{t},t) is regressed onto the pairing direction (rectified flow) and integrated with an Euler ODE under EMA weights. Two flows, Fb→mF_{b\to m} and Fm→bF_{m\to b} , yield a risk score, per-patient counterfactuals, and population attribution, each evaluated against supervised or naive baselines.
 Tabular (MLP)Image (U-Net)
input3030 -vector1×28×281{\times}28{\times}28
width / channels256256 hidden4848 base ch.
time embeddingsinusoidal, 6464sinusoidal, 128128
training steps6000600030003000
batch size256256128128
learning rate10−310^{-3}2×10−42{\times}10^{-4}
Table 1. Architecture and training settings.
CouplingMean L2L_{2} editAttribution rr
Independent (random)25.325.3−0.03-0.03
Optimal transport9.60.49
Table 2. Effect of the coupling on the tabular flow (all else fixed).
Figure 2. Left: ROC curves for malignancy detection. Right: AUROC. The unsupervised transport score (0.91) beats the naive distance baseline (0.88) but not supervised logistic regression (0.99).
MethodValidityL2L_{2} editPlausibilityEdit cos-sim
OT rectified flow0.8419.574.420.64
Mean-shift1.0006.142.991.00
Table 3. Counterfactual quality (benign →\to malignant). Lower plausibility is better; cosine similarity of 1.0 means every patient receives an identical edit.
Figure 3. Counterfactual for the most malignant-looking benign patient. The flow pushes exactly the biomarkers a pathologist expects—larger, more concave, more irregular nuclei—flipping the classifier’s probability.
Figure 4. Left: mean transport displacement per biomarker. Right: flow attribution versus logistic-regression coefficients ( r=0.49r{=}0.49 ). The two label-agnostic and supervised views agree on the malignancy signature.
Figure 5. Benign patients (green) transported into the malignant cloud (red) along the learned flow, projected to two principal components—a direct picture of “pathology transport”.
MethodValid.Prox.#featPlaus.Needs clf.
OT flow (ours)0.858.94263.94no
Wachter0.851.93163.35yes
Mean-shift1.006.14252.99no †
Table 4. Counterfactual methods (benign →\to malignant, seed 0). Proximity/#feat measure edit size and sparsity; plausibility is 1-NN distance to real malignant data (lower is better).
Figure 6. Image risk score ∥x−Fp→n(x)∥\|x-F_{p\to n}(x)\| (edit-distance-to-normal). The unsupervised transport score (AUROC 0.67) beats naive mean-intensity (0.58) but not a supervised pixel classifier (0.93)—the same pattern as the tabular cohort.
Figure 7. Top: integrating Fn→pF_{n\to p} synthesises disease—a healthy lung progressively fills with haze (consolidation). Bottom: for real pneumonia inputs, Fp→n(x)−xF_{p\to n}(x)-x shows what the flow removes to normalise the lung; the signal (blue) concentrates in the lung fields (its faithfulness is examined in Section 7 ).
MethodPointing gameIoUMass-in-lesion
Transport, population0.170.140.13
Sparse counterfactual ( L1L_{1} )0.080.020.06
Normal-manifold AE (label-free)0.390.200.19
Grad-CAM (supervised)0.570.280.27
Random0.140.060.11
Table 5. Localization on synthetic lesions, ground truth known ( N=200N{=}200 ; higher is better). The population transport is near-random; a label-free normal-manifold autoencoder recovers most of the gap to supervised Grad-CAM.
Figure 8. Lesion-focused variants vs population transport (green circle = true lesion). The identity-preserving normal-manifold autoencoder (middle row) concentrates on the lesion, whereas the sparse counterfactual (top) and the population transport (bottom) scatter and miss it.
Figure 9. Scaling the same label-free normal-manifold autoencoder to 128×128128{\times}128 (top) tightly localises the synthetic lesion (green), reaching pointing game 0.520.52 / IoU 0.360.36 ; a simple supervised Grad-CAM (bottom) does not localise focal opacities at this resolution.
MethodPointing gameIoUMass-in-box
Normal-manifold AE (label-free)0.110.110.18
Grad-CAM (supervised)0.300.150.22
Random0.180.100.17
Table 6. Localization on real RSNA lesion boxes ( 8080 held-out positives; higher is better). The label-free autoencoder that worked on synthetic lesions is now no better than random; only supervised saliency exceeds chance.
Figure 10. Real-lesion localisation on RSNA Pneumonia (green = radiologist bounding box). On real chest X-rays the label-free autoencoder (top) no longer concentrates on the lesion; a supervised Grad-CAM (bottom) does modestly better, but the task remains hard.
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