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With similar techniques to the semi-classical high energy descriptions such as the Color Glass Condensate effective framework, we build an interpolating formula between the Bjorken regime and the saturated Regge limit of exclusive Compton Scattering processes (DDVCS and its DVCS and TCS limits). We find a new operator definition for an unintegrated gluon Generalized Parton Distribution, factorized in such a way that the Feynman x dependence is explicit in both the hard and the hadronic matrix elements. We obtain a compact factorized master formula that can be used as a top-down approach to collinear logarithms in the CGC.