  We introduce Support Decomposition Variational Inference (SDVI), a new
variational inference (VI) approach for probabilistic programs with stochastic
support. Existing approaches to this problem rely on designing a single global
variational guide on a variable-by-variable basis, while maintaining the
stochastic control flow of the original program. SDVI instead breaks the
program down into sub-programs with static support, before automatically
building separate sub-guides for each. This decomposition significantly aids in
the construction of suitable variational families, enabling, in turn,
substantial improvements in inference performance.
