Biclustering of transcriptomic data groups genes and samples simultaneously. It is emerging as a standard tool for extracting knowledge from gene expression measurements. We propose a novel generative approach for biclustering called FABIA: Factor Analysis for Bicluster Acquisition. FABIA is based on a multiplicative model, which accounts for linear dependencies between gene expression and conditions, and also captures heavy-tailed distributions as observed in real-world transcriptomic data. The generative framework allows to utilize well-founded model selection methods and to apply Bayesian techniques.