The dynamic Schrödinger bridge problem provides an appealing setting for solving constrained time-series data generation tasks posed as an iteration over optimal transport problems. Recent works have demonstrated state-of-the-art results but are limited to learning bridges with only initial and terminal constraints. Our work extends this paradigm by proposing the Iterative Smoothing Bridge (ISB). We integrate Bayesian filtering and optimal control into learning the diffusion process, enabling constrained stochastic processes governed by sparse observations at intermediate stages and terminal constraints, and assess the effectiveness of ISB on a single-cell embryo RNA data set.