Humans perceive the seemingly chaotic world in a structured and compositional way with the prerequisite of being able to segregate conceptual entities from the complex visual scenes. The mechanism of grouping basic visual elements of scenes into conceptual entities is termed as perceptual grouping. In this work, we propose a new type of spatial mixture models with learnable priors for perceptual grouping. Different from existing methods, the proposed method disentangles the attributes of an object into ``shape'' and ``appearance'' which are modeled separately by the mixture weights and the mixture components. More specifically, each object in the visual scene is fully characterized by one latent representation, which is in turn transformed into parameters of the mixture weight and the mixture component by two neural networks. The mixture weights focus on modeling spatial dependencies (i.e., shape) and the mixture components deal with intra-object variations (i.e., appearance). In addition, the background is separately modeled as a special component complementary to the foreground objects. Our extensive empirical tests on two perceptual grouping datasets demonstrate that the proposed method outperforms the state-of-the-art methods under most experimental configurations. The learned conceptual entities are generalizable to novel visual scenes and insensitive to the diversity of objects. Code is available at https://github.com/jinyangyuan/learnable-deep-priors.