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Proton radiography is used in various high-energy-density (HED) plasma experiments. In this paper, we describe a Monte Carlo and ray-tracing simulation tool called MPRAD that can be used for modeling the deflection of proton beams in arbitrary three dimensional electromagnetic fields, as well as the diffusion of the proton beams by Coulomb scattering and stopping power. The Coulomb scattering and stopping power models in cold matter and fully ionized plasma are combined using interpolation. We discuss the application of MPRAD in a few setups relevant to HED plasma experiments where the plasma density can play a role in diffusing the proton beams and affecting the prediction and interpretation of the proton images. It is shown how the diffusion due to plasma density can affect the resolution and dynamical range of the proton radiography.