Sample Matching for Joint Extinction Gradient Estimation in Differentiable Volume Rendering

Differentiable volume rendering enables gradient-based optimization of volumetric scenes, but unbiased estimators suffer from high gradient variance. We observe that the extinction gradients split into two components on structurally different integration domains: a scattering term evaluated at a single path vertex, and a transmittance term integrated along the ray segment. Because the domains are mismatched, existing estimators sample the two components at different locations, leaving the negative correlation between their opposite-signed contributions unexploited. We expose this overlooked correlation and exploit it through a principle we call sample matching : evaluate both components at shared sample locations. To enable this, we derive the first reformulation of the differential path integral that couples the two contributions within a single integrand, yielding an unbiased Monte Carlo estimator that ties them together by construction. For efficiency, the estimator reuses partially sampled light paths and amortizes in-scattering cost by evaluating gradients at multiple probe points per segment. On voxel-grid reconstruction, our estimator reduces gradient variance by up to 80% over differential ratio tracking (DRT), yielding faster convergence and higher reconstruction quality.