it is known that there are factors of iid for the free ising model on the d-regular tree when it has a unique gibbs measure and not when reconstruction holds (when it is not extremal). we construct a factor of iid for the free ising model on the d-regular tree in (part of) its intermediate regime, where there is non-uniqueness but still extremality. the construction is via the limit of a system of stochastic differential equations. \\ \\ this is a joint work with danny nam and allan sly.