Abstract: Physically-based light transport in heterogeneous volumetric data is computationally expensive because the rendering integral (particularly visibility) has to be stochastically solved. We present a visibility estimation method in concert with an importance-sampling technique for efficient and unbiased stochastic volume rendering. Our solution relies on a joint strategy, which involves the environmental illumination and visibility inside of the volume. A major contribution of our method is a fast sweeping-plane algorithm to progressively estimate partial occlusions at discrete locations, where we store the result using an octahedral representation. We then rely on a quadtree-based hierarchy to perform a joint importance sampling. Our technique is unbiased, requires little precomputation, is highly parallelizable, and is applicable to a various volume data sets, dynamic transfer functions, and changing environmental lighting.