We present a collection of explicit diffusion approximations to small temperature Schrödinger bridges. In the case when both marginals are the same, the setting we consider includes manifold-valued diffusions and Schrödinger bridges computed with respect to reversible reference diffusions. By choosing the underlying space to be a Hessian manifold, this approach gives an explicit diffusion approximation to the Euclidean Schrödinger bridge with different marginals. Joint work with Soumik Pal.