# Learning Multiple-Scattering Solutions for Sphere-Tracing of Volumetric Subsurface Effects

arXiv: https://arxiv.org/abs/2011.03082 · HTML: https://mlsanity.com/paper/2011.03082/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2020.

## Built on by (most cited first, 3 of 3)

- [Deep and Fast Approximate Order Independent Transparency](https://mlsanity.com/paper/2305.10197/) (2023)
- [A real-time rendering method for high albedo anisotropic materials with multiple scattering](https://mlsanity.com/paper/2401.14051/) (2024)
- [Real-time Neural Six-way Lightmaps](https://mlsanity.com/paper/2604.03748/) (2026)

## Abstract (arXiv)

Accurate subsurface scattering solutions require the integration of optical material properties along many complicated light paths. We present a method that learns a simple geometric approximation of random paths in a homogeneous volume of translucent material. The generated representation allows determining the absorption along the path as well as a direct lighting contribution, which is representative of all scattering events along the path. A sequence of conditional variational auto-encoders (CVAEs) is trained to model the statistical distribution of the photon paths inside a spherical region in presence of multiple scattering events. A first CVAE learns to sample the number of scattering events, occurring on a ray path inside the sphere, which effectively determines the probability of the ray being absorbed. Conditioned on this, a second model predicts the exit position and direction of the light particle. Finally, a third model generates a representative sample of photon position and direction along the path, which is used to approximate the contribution of direct illumination due to in-scattering. To accelerate the tracing of the light path through the volumetric medium toward the solid boundary, we employ a sphere-tracing strategy that considers the light absorption and is able to perform statistically accurate next-event estimation. We demonstrate efficient learning using shallow networks of only three layers and no more than 16 nodes. In combination with a GPU shader that evaluates the CVAEs' predictions, performance gains can be demonstrated for a variety of different scenarios. A quality evaluation analyzes the approximation error that is introduced by the data-driven scattering simulation and sheds light on the major sources of error in the accelerated path tracing process.