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CyclOT: Learning Quadratic Optimal Transport Maps via Synchronized Forward-Backward Interpolants

arXiv · AI, language, vision and robotics · article · Sep 12, 2026 · UTC

We study the recovery of forward and reverse quadratic optimal-transport maps from unpaired samples in high dimensions. We introduce a bidirectional neural framework in which the learned maps induce forward and backward displacement interpolants, while the training objective combines bidirectional quadratic action, discriminator-restricted Jensen-Shannon endpoint objectives, and two-sided cycle consistency. The construction requires neither precomputed sample pairings nor an explicit convex-potential parameterization. For absolutely continuous probability measures supported on a compact convex

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