  Preserving individual privacy while enabling collaborative data sharing is
crucial for organizations. Synthetic data generation is one solution, producing
artificial data that mirrors the statistical properties of private data. While
numerous techniques have been devised under differential privacy, they
predominantly assume data is centralized. However, data is often distributed
across multiple clients in a federated manner. In this work, we initiate the
study of federated synthetic tabular data generation. Building upon a SOTA
central method known as AIM, we present DistAIM and FLAIM. We first show that
it is straightforward to distribute AIM, extending a recent approach based on
secure multi-party computation which necessitates additional overhead, making
it less suited to federated scenarios. We then demonstrate that naively
federating AIM can lead to substantial degradation in utility under the
presence of heterogeneity. To mitigate both issues, we propose an augmented
FLAIM approach that maintains a private proxy of heterogeneity. We simulate our
methods across a range of benchmark datasets under different degrees of
heterogeneity and show we can improve utility while reducing overhead.
