Discontinuous visibility changes remain a major bottleneck when optimizing surfaces within a physically based inverse renderer. Many previous works have proposed sophisticated algorithms and data structures to sample visibility silhouettes more efficiently.

Our work presents another solution: instead of evolving a surface locally, we extend differentiation to hypothetical surface patches anywhere in 3D space. We refer to this as a “many-worlds” representation because it models a superposition of independent surface hypotheses that compete to explain the reference images. These hypotheses do not interact through shadowing or scattering, leading to a new transport law that distinguishes our method from prior work based on exponential random media.

The complete elimination of visibility-related discontinuity handling bypasses the most complex and costly component of prior inverse rendering methods, while the extended derivative domain promotes rapid convergence. We demonstrate that the resulting Monte Carlo algorithm solves physically based inverse problems with both reduced per-iteration cost and fewer total iterations.