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Significant advances have been made in modeling the intense beams of heavy-ion beam-driven Inertial Fusion Energy (Heavy Ion Fusion). In this paper, a roadmap for a validated, predictive driver simulation capability, building on improved codes and experimental diagnostics, is presented, as are examples of progress. The Mesh Refinement and Particle-in-Cell methods were integrated in the WARP code; this capability supported an injector experiment that determined the achievable current rise time, in good agreement with calculations. In a complementary effort, a new injector approach based on the merging of ≈100 small beamlets was simulated, its basic feasibility established, and an experimental test designed. Time-dependent 3D simulations of the High Current Experiment (HCX) were performed, yielding voltage waveforms for an upcoming study of bunch-end control. Studies of collective beam modes which must be taken into account in driver designs were carried out. The value of using experimental data to tomographically ''synthesize'' a 4D beam particle distribution and so initialize a simulation was established; this work motivated further development of new diagnostics which yield 3D projections of the beam phase space. Other developments, including improved modeling of ion beam focusing and transport through the fusion chamber environment and onto the target, and of stray electrons and their effects on ion beams, are briefly noted.