We present our submission to the Extreme Value Analysis 2021 Data Challenge in which teams were asked to accurately predict distributions of wildfire frequency and size within spatio-temporal regions of missing data. For the purpose of this competition we developed a variant of the powerful variational autoencoder models dubbed the Conditional Missing data Importance-Weighted Autoencoder (CMIWAE). Our deep latent variable generative model requires little to no feature engineering and does not necessarily rely on the specifics of scoring in the Data Challenge. It is fully trained on incomplete data, with the single objective to maximize log-likelihood of the observed wildfire information. We mitigate the effects of the relatively low number of training samples by stochastic sampling from a variational latent variable distribution, as well as by ensembling a set of CMIWAE models trained and validated on different splits of the provided data. The presented approach is not domain-specific and is amenable to application in other missing data recovery tasks with tabular or image-like information conditioned on auxiliary information.