We propose a novel multi-conditional latent variable model for simultaneous facial feature fusion and detection of facial action units. In our approach we exploit the structure-discovery capabilities of generative models such as Gaussian processes, and the discriminative power of classifiers such as logistic function. This leads to superior performance compared to existing classifiers for the target task that exploit either the discriminative or generative property, but not both. The model learning is performed via an efficient, newly proposed Bayesian learning strategy based on Monte Carlo sampling. Consequently, the learned model is robust to data overfitting, regardless of the number of both input features and jointly estimated facial action units. Extensive qualitative and quantitative experimental evaluations are performed on three publicly available datasets (CK+, Shoulder-pain and DISFA). We show that the proposed model outperforms the state-of-the-art methods for the target task on (i) feature fusion, and (ii) multiple facial action unit detection.