We propose an adaptive sampling and reconstruction method for offline Monte Carlo rendering. Our method produces sampling maps constrained by a user-defined budget that minimize the expected future denoising error. Compared to other state-of-the-art methods, which produce the necessary training data on the fly by composing pre-rendered images, our method samples from analytic noise distributions instead. These distributions are compact and closely approximate the pixel value distributions stemming from Monte Carlo rendering. Our method can efficiently sample training data by leveraging only a few per-pixel statistics of the target distribution, which provides several benefits over the current state of the art. Most notably, our analytic distributions' modeling accuracy and sampling efficiency increase with sample count, essential for high-quality offline rendering. Although our distributions are approximate, our method supports joint end-to-end training of the sampling and denoising networks. Finally, we propose the addition of a global summary module to our architecture that accumulates valuable information from image regions outside of the network's receptive field. This information discourages sub-optimal decisions based on local information. Our evaluation against other state-of-the-art neural sampling methods demonstrates denoising quality and data efficiency improvements.