We present a compact, learning-based representation that captures the full Monte Carlo sampling distribution of a rendered image. Our approach enables rendering at arbitrary samples per pixel (SPP) during inference without requiring expensive path tracing operations. This is achieved by fitting parametric distributions to per-pixel radiance values, which can be efficiently estimated, stored, and sampled. Our method proceeds in three stages. First, we map radiance samples into radial log space, which encourages Gaussian-like distributions while preserving angular relationships. Second, we fit each pixel’s distribution using 3D Gaussian Mixture Models (GMMs), trained online with minimal memory overhead, making the approach compatible with standard path tracers. For inference, we introduce an optimized sampling scheme whose complexity is independent of the target SPP, enabling fast synthesis of high-SPP images. Additionally, we demonstrate that the learned representations can be heavily compressed using quantization and codebook techniques with negligible quality loss. Experiments show that GMMs strike an effective balance between expressiveness and sparsity. Compared to alternative models, our method better captures pixel-wise Monte Carlo distributions. Lastly, we illustrate the versatility of our representation with applications such as firefly rejection and ray-distribution-driven denoising.