This paper derives the generalized extreme value (GEV) model with implicit availability/perception (IAP) of alternatives and proposes a variational autoencoder (VAE) approach for choice set generation and implicit perception of alternatives. Specifically, the cross-nested logit (CNL) model with IAP is derived as an example of IAP-GEV models. The VAE approach is adapted to model the choice set generation process, in which the likelihood of perceiving chosen alternatives in the choice set is maximized. The VAE approach for route choice set generation is exemplified using a real dataset. IAP- CNL model estimated has the best performance in terms of goodness-of-fit and prediction performance, compared to multinomial logit models and conventional choice set generation methods.