Latent factor models offer a very useful framework for modeling dependencies in high-dimensional multivariate data. In this work we investigate a class of latent factor models with hidden noisy-or units that let us decouple high dimensional vector of observable binary random variables using a 'small' number of hidden binary factors. Since the problem of learning of such models from data is intractable, we develop its variational approximations. We present and analyze two versions of the variational learning method, each with a different assumption placed on free parameters of the approximation and consequently with a different computation/accuracy tradeoff. We test the two learning methods and their combination on a suite of noisy-or networks and illustrate their respective advantages.