Abstract: We propose a technique to build the irradiance cache for isotropic scattering simultaneously with Monte Carlo progressive direct volume rendering on a single GPU, which allows us to achieve up to four times increased convergence rate for complex scenes with arbitrary sources of light. We use three procedures that run concurrently on a single GPU. The first is the main rendering procedure. The second procedure computes new cache entries, and the third one corrects the errors that may arise after creation of new cache entries. We propose two distinct approaches to allow massive parallelism of cache entry creation. In addition, we show a novel extrapolation approach which outputs high quality irradiance approximations and a suitable prioritization scheme to increase the convergence rate by dedicating more computational power to more complex rendering areas.