One of the main achievements of loop quantum gravity is the consistent quantization of the analog of the Wheeler-DeWitt equation which is free of ultra-violet divergences. However, ambiguities associated to the intermediate regularization procedure lead to an apparently infinite set of possible theories. The absence of an UV problem---the existence of well behaved regularization of the constraints---is intimatelly linked with the ambiguities arising in the quantum theory. Among these ambiguities there is the one associated to the $SU(2)$ unitary representation used in the diffeomorphism covariant point-splitting'' regularization of the non linear functionals of the connection. This ambiguity is labelled by a half-integer $m$ and, here, it is referred to as the {\em $m$-ambiguity}. I will ellaborate on this issue and show some results that suggest that the degree of ambiguity is reduced when considering the dynamics in the corresponding theory.