  Reconciling symbolic and distributed representations is a crucial challenge
that can potentially resolve the limitations of current deep learning.
Remarkable advances in this direction have been achieved recently via
generative object-centric representation models. While learning a recognition
model that infers object-centric symbolic representations like bounding boxes
from raw images in an unsupervised way, no such model can provide another
important ability of a generative model, i.e., generating (sampling) according
to the structure of learned world density. In this paper, we propose Generative
Neurosymbolic Machines, a generative model that combines the benefits of
distributed and symbolic representations to support both structured
representations of symbolic components and density-based generation. These two
crucial properties are achieved by a two-layer latent hierarchy with the global
distributed latent for flexible density modeling and the structured symbolic
latent map. To increase the model flexibility in this hierarchical structure,
we also propose the StructDRAW prior. In experiments, we show that the proposed
model significantly outperforms the previous structured representation models
as well as the state-of-the-art non-structured generative models in terms of
both structure accuracy and image generation quality. Our code, datasets, and
trained models are available at https://github.com/JindongJiang/GNM
