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In this article, we propose a novel online framework to learn the spatial-varying distribution of the full product of the rendering equation, with a single small neural network using stochastic ray samples. The learned distributions can be used to efficiently sample the full product of incident light. To accomplish this, we introduce a novel closed-form density model, called the Normalized Anisotropic Spherical Gaussian mixture, that can model a complex light field with a small number of parameters and that can be directly sampled. Our framework progressively renders and learns the distribution, without requiring any warm-up phases. With the compact and expressive representation of our density model, our framework can be implemented entirely on the GPU, allowing it to produce high-quality images with limited computational resources. 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