Fast and realistic synthesis of real videos with computer generated content has been a challenging problem in computer graphics. It involves computationally expensive light transport calculations. We present a novel and efficient algorithm for diffuse light transport calculation between virtual and real worlds called Differential Irradiance Caching. Our algorithm produces a high-quality result while preserving interactivity and allowing dynamic geometry, materials, lighting, and camera movement. The problem of expensive differential irradiance evaluation is solved by exploiting the spatial coherence in indirect illumination using irradiance caching. We enable multiple bounces of global illumination by using Monte Carlo integration in GPU ray-tracing to evaluate differential irradiance at irradiance cache records in one pass. The combination of ray-tracing and rasterization is used in an extended irradiance cache splatting algorithm to provide a fast GPU-based solution of indirect illumination. Limited information stored in the irradiance splat buffer causes errors for pixels on edges in case of depth of field rendering. We propose a solution to this problem using a reprojection technique to access the irradiance splat buffer. A novel cache miss detection technique is introduced which allows for a linear irradiance cache data structure. We demonstrate the integration of differential irradiance caching into a rendering framework for Mixed Reality applications capable of simulating complex global illumination effects.