People can learn rich, general-purpose conceptual representations from only\nraw perceptual inputs. Current machine learning approaches fall well short of\nthese human standards, although different modeling traditions often have\ncomplementary strengths. Symbolic models can capture the compositional and\ncausal knowledge that enables flexible generalization, but they struggle to\nlearn from raw inputs, relying on strong abstractions and simplifying\nassumptions. Neural network models can learn directly from raw data, but they\nstruggle to capture compositional and causal structure and typically must\nretrain to tackle new tasks. We bring together these two traditions to learn\ngenerative models of concepts that capture rich compositional and causal\nstructure, while learning from raw data. We develop a generative neuro-symbolic\n(GNS) model of handwritten character concepts that uses the control flow of a\nprobabilistic program, coupled with symbolic stroke primitives and a symbolic\nimage renderer, to represent the causal and compositional processes by which\ncharacters are formed. The distributions of parts (strokes), and correlations\nbetween parts, are modeled with neural network subroutines, allowing the model\nto learn directly from raw data and express nonparametric statistical\nrelationships. We apply our model to the Omniglot challenge of human-level\nconcept learning, using a background set of alphabets to learn an expressive\nprior distribution over character drawings. In a subsequent evaluation, our GNS\nmodel uses probabilistic inference to learn rich conceptual representations\nfrom a single training image that generalize to 4 unique tasks, succeeding\nwhere previous work has fallen short.\n