EviFlow: Structured-Noise Flow Matching for Multi-Rater Segmentation

Multi-rater segmentation requires coherent alternative delineations, not merely variable pixelwise predictions. We introduce EviFlow, a conditional flow-matching sampler driven by spatially coherent base noise, together with a distribution-aware evaluation protocol. We establish that, for binary masks on a fixed finite grid, the generalized energy distance (GED) with ground distance is exactly the squared maximum mean discrepancy under the Jaccard kernel. Its strict positive definiteness makes this GED a strictly proper population divergence; the variant with ground distance is strictly proper as well. We distinguish these population guarantees from U- and V-statistic estimation and complement GED with Hungarian-matched IoU (HM-IoU), dispersion, and simple stochastic references. Replacing independent base noise with normalized blurred Gaussian noise yields coherent whole-object alternatives: on LIDC-IDRI with four raters and nine seeds, energy GED decreases from 0.178±0.014 to 0.092±0.022 and HM-IoU rises from 0.361±0.027 to 0.489±0.029. Baseline tuning changes the comparison substantially: a validation-tuned Probabilistic U-Net is not significantly different on energy GED and is better on Jaccard MMD and HM-IoU, whereas its untuned counterpart is the weakest learned stochastic baseline on LIDC GED. On LNDb, EviFlow achieves lower energy GED than the tuned Probabilistic U-Net; additional benchmarks reveal dataset-dependent trade-offs. These findings show the value of structured generative noise and establish a practical case for reporting distributional fit, sample fidelity, dispersion, and baseline tuning together.