We seek to understand the quantitative role of the dominant physical processes (charge-exchange, adiabatic heating, stochastic acceleration) governing the proton distribution in the heliotail using observations of hydrogen energetic neutral atoms (ENAs) from the Interstellar Boundary Explorer (IBEX). We solve the Parker transport equation for solar wind protons and pickup ions (PUIs) as they propagate from the termination shock (TS) down the heliotail, including charge-exchange between protons and neutral hydrogen atoms as source terms derived from an MHD-fluid and kinetic-neutral simulation of the heliosphere. We compute ENA fluxes at 1 au from the results of the proton transport model and compare them with IBEX observations. We find that, under the assumptions of our model, a stochastic acceleration process is needed to counteract the energy-dependent losses of ~0.1–5 keV PUIs from charge-exchange to reproduce IBEX data. The power-law velocity dependence of the diffusion coefficient (spectral index γ) is limited to the range 0.67<γ<2, and the best fit to IBEX data appears close to γ~1.25. The diffusion rate ~1.1×10−8 km2 s−3 (v/v0)1.25 nearly balances the loss of ~0.1–5 keV PUIs by charge-exchange. Our analysis suggests that cyclotron resonance with two widely known incompressible MHD turbulence: namely, isotropic Kolmogorov and anisotropic Goldreich–Sridhar turbulence, as well as stochastic particle interactions with compressive waves are not by themselves the dominant diffusion mechanisms. However, some intermediate processes may be occurring due to the presence of PUIs.