Elastic interfaces with varying levels of permeability are widely encountered in nature. Red blood cells, for example, are characterized by an area-incompressible membrane that is permeable to the diffusion of oxygen and carbon dioxide. Artificial capsules, on the other hand, are often engineered to remain impermeable until they reach a designated location or time, whereby they release their internal contents into the surrounding medium. A common approach to numerical simulations of elastic capsules in flow involves discretizing the membrane surface to facilitate the calculation of shear strains and area changes. Recently, level-set-based methods that rely on advection of the reference map between the deformed and reference configurations have proven to be a promising alternative. This approach offers several advantages, including ease of implementation and parallelization. In the present work, we adapt the level-set-based formulation to a diffuse interface framework to overcome the intrinsic limitation of the level-set to conserve mass. We show that by adding a variational term to the reference map advection equation, consistency between the interface location (defined using a reference map) and the diffused interface can be ensured. Through a number of validation cases, we show the accuracy and robustness of the present approach. In addition, we extend the framework to multi-capsule simulations, demonstrating the ability of handling hundreds of discrete capsules with minimal additional computational cost.