Distribution matching with discrete optimal transport flows: Modeling normative brain aging

Matching instances from distinct distributions without direct pairings is a common challenge in biology. Estimating individual trajectories in temporal phenomena can be seen as a form of distribution alignment. We propose a novel medical image-to-image translation method combining optimal transport (OT) with Normalizing Flows (NF). This extends NF’s ability to transform initial distributions into any target distribution accessible via samples. Leveraging the bijectivity of standard NF, the method preserves identity without requiring cycle consistency, while parametrized transformations and access to the probability density function at each step help constrain transformation paths. For efficiency, an autoencoder with Sobel-based perceptual loss reduces image dimensionality before feeding data into the OT-NF model. Evaluated on structural brain images to predict temporal progression, the sliced Wasserstein distance among OT losses best balanced computational efficiency, target approximation, and identity preservation. Our results show the method produces realistic predictions while preserving individual anatomical traits. • Introduce discrete Optimal Transport Flow for unpaired image-to-image translation within the temporal prediction setting. • Enable smooth, controllable trajectories on transformation manifolds. • Compare Sliced Wasserstein variants for quality vs. computation trade-offs. • Use perceptual-dimensionality reduction to project data onto a semantically rich, low-dimensional manifold, improving transport accuracy and efficiency. • Forecast subject-specific brain aging without longitudinal data.