Abstract: In this article we present a novel formulation of progressive photon mapping. Similar to the original progressive photon mapping algorithm, our approach is capable of computing global illumination solutions without bias in the limit, and it uses only a constant amount of memory. It produces high-quality results in situations that are difficult for most other algorithms, such as scenes with realistic light fixtures where the light sources are completely enclosed by refractive material. Our new formulation is based on a probabilistic derivation. The key property of our approach is that it does not require the maintenance of local photon statistics. In addition, our derivation allows for arbitrary kernels in the radiance estimate and includes stochastic ray tracing algorithms. Finally, our approach is readily applicable to volumetric photon mapping. We compare our algorithm to previous progressive photon mapping approaches and show that we achieve the same convergence to unbiased results, even without local photon statistics.