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.

Haptic teleoperation is a promising technology with applications in telemaintenance and disaster management. However, it faces significant challenges when the application is subjected to a high network latency and environments with moving objects. This work aims to extend Model Mediated Teleoperation (MMT) to overcome challenges in supporting dynamic environments. Instead of striving for perfect model alignment, we acknowledge the inevitable mismatch between the remote environment and its model at the operator. We propose a set of design principles and an accompanying framework for designing MMT solutions that prioritize operator intent. Our approach is exemplified through an application where an operator, located 8000 km away (The Netherlands – India) and subjected to an average of 179 ms end-to-end latency, guides a robot arm to draw on a whiteboard whose position is actively altered. We evaluate the effectiveness of our approach through a user study. We show a 3-point improvement on a 7-point Likert scale when users utilize our approach to teleoperate over significant network latency of up to 1 second.