Abstract: Mixed cells are introduced in multi-material arbitrary Lagrangian-Eulerian (MMALE) method to capture material interfaces. An energy-preserving closure model on mixed cells for diffusion equation is proposed. Based on closure model, a method for coupling multiple material radiation diffusion simulation and hydrodynamics MMALE simulation is proposed. Numerical experiment with analytical solution shows accuracy of the method for diffusion equation. Results of Sedov and spherical implosion problems show that the method is effective and robust. Comparisons with traditional Lagrangian method prove advantages of the method.