Tsunamis pose a threat to the coastal communities. Typically, tsunami hazards are estimated using computationally expensive numerical models, often impractical for rapidly determining the expected impacts and community response. To quickly estimate tsunami hazards, we present a data-driven transfer function method to reconstruct onshore hazard curves from offshore hazard curves with corresponding topographic data. The transfer function is approximated by a type of artificial neural network called a Variational Autoencoder (VAE). The VAE first encodes input data, including offshore hazard curves and topographic data. Once encoded, the data is represented by a normal distribution of latent variables. The VAE then uses a trained decoder to sample the distribution created by the latent variables and reconstruct a continuous hazard function at the onshore location. As a probabilistic distribution represents the encoded values, the resulting hazard curve output has inherent stochasticity. Thus, model variance can be found through many realizations of the transfer function for a single set of inputs. We developed a set of transfer functions to accurately predict the onshore hazard curves for flow depth, Froude number (dimensionless velocity), and dimensionless momentum flux. We construct two flow depth transfer functions, with one version utilizing an ”anchor point” taken from established site-specific numerical modeling data. The VAEs to predict velocity and momentum flux incorporate an approach that leverages condensed topographic information around the point of interest (topographic rings). Overall, the transfer function method efficiently estimates onshore tsunami hazard curves and model uncertainty quantification without requiring computationally expensive numerical simulations.