This chapter derives Gauss-NewtonGauss-Newtonmethod and Levenberg-Marquardt methods for RML sampling that searches for the solution in the ensemble subspace. The approach does not introduce any further assumptions since ensemble methods implicitly confine the solution to the space spanned by the prior ensemble. The advantage of the ensemble subspace formulation is that it avoids the inversion of huge low-rank covariance matrices and solves the EnRML formulation precisely without introducing any further approximations. The subspace EnRML algorithm can also compute the posterior ensemble subspaceEnsemblesubspace solution for the ES and ESMDA methods.