Score-based diffusion built intrinsically on the quantum pure-state manifold CP^{d-1}, trained with a local-time Gaussian teacher, matches pure-state ensembles far better than Euclidean baselines in the local-cluster regime, with gains shrinking on globally spread ensembles.
International Conference on Learning Representations , year=
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A single-objective rectified flow variant uses neural ODEs trained by regression to monotonically decrease a fixed convex transport cost while preserving marginal distributions.
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Local-Time Riemannian Score Matching on the Quantum Pure-State Manifold
Score-based diffusion built intrinsically on the quantum pure-state manifold CP^{d-1}, trained with a local-time Gaussian teacher, matches pure-state ensembles far better than Euclidean baselines in the local-cluster regime, with gains shrinking on globally spread ensembles.
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Rectified Flow: A Marginal Preserving Approach to Optimal Transport
A single-objective rectified flow variant uses neural ODEs trained by regression to monotonically decrease a fixed convex transport cost while preserving marginal distributions.