Recent progress in inverse rendering has been driven in large part by methods based on emissive volumes. These methods are robust and scalable, but they place only weak constraints on the physical meaning of the reconstruction. At the other extreme, inverse rendering with explicit surfaces and physically based light transport aims to recover geometry, materials, and lighting with direct physical meaning, but is much harder because visibility changes are discontinuous, Monte Carlo estimates are noisy, and unknown scene factors are tightly coupled.

This thesis focuses on that harder setting, while studying it in relation to nearby formulations that are easier to optimize. It views inverse rendering along two continua: geometry representations, ranging from volumes to explicit surfaces, and image formation models, ranging from stored radiance to physically based transport.

First, the thesis revisits derivatives for physically based surface rendering and derives a simple local formulation of visibility-related terms. This leads to Projective Sampling, which reuses primal transport samples to guide boundary sampling and improves the efficiency of geometry derivatives.

Second, it introduces a distribution-over-surfaces viewpoint that relaxes geometric optimization without giving up a surface output. In the physically based setting, Many-Worlds Inverse Rendering extends surface derivatives into space by evaluating hypothetical surface patches as competing explanations of the observations. In the emissive setting, Radiance Surfaces replaces image-space supervision of radiance volumes with a 5D radiance field loss that more directly encourages convergence to explicit surfaces while retaining much of the speed and robustness of NeRF-style optimization.

Third, the thesis explores intermediate formulations between emissive and fully physically based inversion. Radiance Caching for Differentiable Path Tracing uses a spatially varying blend between cached and material-based estimators to improve robustness for material estimation under unknown illumination. Together, these results suggest that inverse rendering is best understood not as a choice between disconnected methods, but as a continuum of trade-offs. By clarifying derivative transport and developing algorithms that move along these continua in controlled ways, this thesis makes physically meaningful inverse rendering more robust in practice.