Gradient-domain rendering estimates image-space gradients using correlated sampling, which can be combined with color information to reconstruct smoother and less noisy images. While simple ℒ 2 reconstruction is unbiased, it often leads to visible artifacts. In contrast, most recent reconstruction methods based on learned or handcrafted techniques improve visual quality but introduce bias, leaving the development of practically unbiased reconstruction approaches relatively underexplored. In this work, we propose a generalized framework for unbiased reconstruction in gradient-domain rendering. We first derive the unbiasedness condition under a general formulation that linearly combines pixel colors and gradients. Based on this unbiasedness condition, we design a practical algorithm 1 that minimizes image variance while strictly satisfying unbiasedness. Experimental results demonstrate that our method not only guarantees unbiasedness but also achieves superior quality compared to existing unbiased and slightly biased reconstruction methods.

Photon mapping is a fundamental and practical Monte Carlo rendering technique for efficiently simulating global illumination effects, especially for caustics and specular-diffuse-specular (SDS) paths. In this paper, we present the first differentiable rendering method for photon mapping. The core of our method is a newly introduced concept named generalized path gradients. Based on the extended path space manifolds (EPSMs) [Xing et al. 2023], the generalized path gradients define the derivatives of the vertex positions and color contributions of a path with respect to scene parameters under given geometric constraints. By formalizing photon mapping as a path sampling technique through vertex merging [Georgiev et al. 2012] and incorporating a smooth differentiable density estimation kernel, we enable the differentiation of the photon mapping algorithms based on the theoretical results of generalized path gradients. Experiments demonstrate that our method is more effective than state-of-the-art physics-based differentiable rendering methods in inverse rendering applications involving difficult illumination paths, especially SDS paths.