Local-Time Riemannian Score Matching on the Quantum Pure-State Manifold
Score-based diffusion can be defined intrinsically on the manifold of quantum pure states, $\mathbb{CP}^{d-1}$ with the Fubini--Study metric, but no closed-form transition density is available, so the score must be supervised by a local-time teacher taken from the Euclidean limit of the diffusion in normal coordinates. This paper is about what makes that teacher work, and where it stops working. Three training choices turn out not to be incidental: the increment must be divided by the diffusion clock rather than by the elapsed time, since the published expression assumes unit diffusion and a non-unit schedule introduces a time-change mismatch varying by a factor of $400$ across the horizo...
| Authors | Jian Xu, Wei Chen, Shigui Li et al. |
|---|---|
| Primary category | stat.ML |
| Published | 5 May 2026 |
| Last updated at source | 2 August 2026 |
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