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Beyond Gradient Flow: Identifiability and Recovery from Distribution Snapshots
Inferring dynamics from snapshots of evolving distributions is fundamentally underdetermined: the Fokker-Planck equation constrains the drift $F$ only through its score-weighted divergence $\nabla\cdot F+F\cdot\nabla\logρ$, leaving a $ρ$-solenoidal gauge invisible to any single-time constraint. Time
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