In this article we consider a family of real-valued diffusion processes on the time interval [0; 1] indexed by their prescribed initial value and another point y in space. We first present a condition on their drift and diffusion coefficients ensuring that the diffusion is pinned in y at time 1. Our main result then concerns the following question: can this family of pinned diffusions be obtained as the bridges either of a Gaussian Markov process or of an Ito diffusion? We eventually illustrate our precise answer with several examples.