[en] We introduce a new model of near-forward elastic proton–(anti)proton scattering at high energy based on the modern formulation of Pomeron and Odderon in terms of Wilson lines and generalized transverse momentum dependent distributions. We compute the helicity-dependent elastic amplitudes ϕ${}_{1,2,3,4,5}$ in this model and study their energy dependence from the nonlinear small-x evolution equations. While both Pomeron and Odderon contribute to helicity-flip processes in general, in the forward limit t = 0 only the double helicity-flip amplitude ϕ${}_2$, dominated by the spin-dependent Odderon, survives. This may affect the extraction of the ρ parameter as well as the total cross section in the LHC energy domain and beyond.