  Synthetic data has been hailed as the silver bullet for privacy preserving
data analysis. If a record is not real, then how could it violate a person's
privacy? In addition, deep-learning based generative models are employed
successfully to approximate complex high-dimensional distributions from data
and draw realistic samples from this learned distribution. It is often
overlooked though that generative models are prone to memorising many details
of individual training records and often generate synthetic data that too
closely resembles the underlying sensitive training data, hence violating
strong privacy regulations as, e.g., encountered in health care. Differential
privacy is the well-known state-of-the-art framework for guaranteeing
protection of sensitive individuals' data, allowing aggregate statistics and
even machine learning models to be released publicly without compromising
privacy. The training mechanisms however often add too much noise during the
training process, and thus severely compromise the utility of these private
models. Even worse, the tight privacy budgets do not allow for many training
epochs so that model quality cannot be properly controlled in practice. In this
paper we explore an alternative approach for privately generating data that
makes direct use of the inherent stochasticity in generative models, e.g.,
variational autoencoders. The main idea is to appropriately constrain the
continuity modulus of the deep models instead of adding another noise mechanism
on top. For this approach, we derive mathematically rigorous privacy guarantees
and illustrate its effectiveness with practical experiments.
