We combine hierarchical Bayesian modeling with a flow-based deep generative network, in order to demonstrate that one can efficiently constraint numerical gravitational-wave (GW) population models at a previously intractable complexity. Existing techniques for comparing data to simulation, such as discrete model selection and Gaussian process regression, can only be applied efficiently to moderate-dimension data. This limits the number of observable (e.g., chirp mass, spins.) and hyperparameters (e.g., common envelope efficiency) one can use in a population inference. In this study, we train a network to emulate a phenomenological model with 6 observables and 4 hyper-parameters, use it to infer the properties of a simulated catalogue and compare the results to using a phenomenological model. We find that a 10-layer network can emulate the phenomenological model accurately and efficiently. Our machine enables simulation-based GW population inferences to take on data at a new complexity level.