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.

Abstract We describe a method to use Spherical Gaussians with free directions and arbitrary sharpness and amplitude to approximate the precomputed local light field for any point on a surface in a scene. This allows for a high‐quality reconstruction of these light fields in a manner that can be used to render the surfaces with precomputed global illumination in real‐time with very low cost both in memory and performance. We also extend this concept to represent the illumination‐weighted environment visibility , allowing for high‐quality reflections of the distant environment with both surface‐material properties and visibility taken into account. We treat obtaining the Spherical Gaussians as an optimization problem for which we train a Convolutional Neural Network to produce appropriate values for each of the Spherical Gaussians' parameters. We define this CNN in such a way that the produced parameters can be interpolated between adjacent local light fields while keeping the illumination in the intermediate points coherent.