Generation Properties of Stochastic Interpolation under Finite Training Set

The paper presents a theoretical analysis of generative models operating under finite training sets within the stochastic interpolation framework. It derives closed-form expressions for the optimal velocity field and score function, showing that the deterministic process recovers training samples while the stochastic process introduces Gaussian noise. This work is significant for practitioners as it provides insights into the effects of model estimation errors on generation quality, offering formal definitions of underfitting and overfitting tailored for generative models, which can inform model design and evaluation in real-world applications.