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Entropic Optimal Transport (EOT) has become a practical framework for learning stochastic couplings between complex distributions, with applications in generative modeling and domain adaptation. However, most EOT solvers are designed for Euclidean spaces, while manifold extensions remain limited and often rely on costl...
This paper proposes a neural method for solving the simultaneous OT problem by learning a shared transport map that minimizes the average transport cost while aligning each source distribution with a prescribed target, and derives a max-min formulation for learning this map.
The Interval Denoiser, a theoretically rigorous framework for latent-free generation, derived directly from the flow matching ODE, establishes an exact analytical mapping for intermediate trajectory states and is shown to reside on a low-dimensional manifold across any time interval.
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