We prove a relative compactness criterion in Wiener-Sobolev space which represents a natural extension of the compact embedding of sobolev space H^1 into L^2, at the level of random fields. Then we give a specific statement of this criterion for random fields solutions of semi-linear Stochastic Partial Differential Equations with coefficients bounded in an appropriate way. Finally, we employ this result to construct solutions for semi-linear Stochastic Partial Differential Equations with distribution as final condition. We also give a probabilistic interpretation of this solution in terms of Backward Doubly Stochastic Differential Equations formulated in a weak sense.