Generation Properties of Stochastic Interpolation
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Generation Properties of Stochastic Interpolation under Finite Training Set
arXiv:2509.21925v2 Announce Type: replace Abstract: This paper investigates the theoretical behavior of generative models under finite training populations. Within the stochastic interpolation generative framework, we derive closed-form expressions for the optimal velocity field and score function when only a finite number of training samples are available. We demonstrate that, under some regularity conditions, the deterministic generative process exactly recovers the training samples, while...