| Abstract: |
| We provide an estimate of Wasserstein distance between data distribution and generation of score-based generative models in the infinite dimensional function space. The bound only assumes the $\epsilon$-accurate approximation of score and Gaussian type tail behavior of the data distribution. The key in the analysis is the Lipchitz bound of the score which relates to the Hessian estimate of a viscous Hamilton Jacobian equation (vHJ). The later is shown by utilizing a kernel estimate that is independent of dimension. Our complexity bound scales linearly with the trace of a covariance operator relates to the data distribution. |
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