# Stochastic Gradient Estimation for Higher-order Differentiable Rendering

arXiv: https://arxiv.org/abs/2412.03489 · HTML: https://mlsanity.com/paper/2412.03489/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2024.

## Built on by (most cited first, 2 of 2)

- [Feature-Guided Diffusion for Non-Differentiable Inverse Rendering](https://mlsanity.com/paper/2607.17411/) (2026)
- [Scene Parameter Saliency via Differentiable Light Transport](https://mlsanity.com/paper/2607.21562/) (2026)

## Abstract (arXiv)

We derive methods to compute higher order differentials (Hessians and Hessian-vector products) of the rendering operator. Our approach is based on importance sampling of a convolution that represents the differentials of rendering parameters and shows to be applicable to both rasterization and path tracing. We further suggest an aggregate sampling strategy to importance-sample multiple dimensions of one convolution kernel simultaneously. We demonstrate that this information improves convergence when used in higher-order optimizers such as Newton or Conjugate Gradient relative to a gradient descent baseline in several inverse rendering tasks.