We construct diffusions on a space of interval partitions of [0,1] that are stationary with Poisson-Dirichlet laws. The processes of ranked interval lengths of our partitions are diffusions introduced by Ethier and Kurtz (1981) and Petrov (2009). Specifically, we decorate the jumps of a spectrally positive stable process with independent squared Bessel excursions. In the spirit of Ray-Knight...