Given a set of input-output examples specifying the behavior of a function, the problem of inductive synthesis is to generate a deterministic program producing the observed outputs on the given inputs. Recent work suggests synthesizing deterministic programs by instead searching over a space of probabilistic programs. The idea is that the marginal likelihood that a probabilistic program produces the observed input-output examples can be used as a measure of how close that probabilistic program is to the deterministic solution. A probabilistic program that accurately captures the high-level structure of a solution will ascribe higher likelihood to the examples. This program can then be iteratively refined, gradually replacing probabilistic components with more and more deterministic structure until a deterministic solution is found. In this abstract, we seek to develop and evaluate synthesis algorithms that draw on this insight along with recent advances in efficient evaluation of exact marginal likelihood. We first explore whether MCMC over a space of probabilistic programs aids in the synthesis of deterministic programs, and subsequently develop and evaluate a sequential Monte Carlo (SMC) algorithm based on the idea of coarse-to-fine refinements.