Physically based rendering is a process for photorealistic digital image synthesis and one of the core problems in computer graphics. It involves simulating the light transport, i.e. the emission, propagation, and scattering of light through a virtual scene that is defined by a detailed description of object geometry and appearance. Research over the last decades has led to sophisticated rendering techniques and recently, the inversion of this process, i.e. recovering scene parameters from image observations, has also received significant attention. In this thesis, we investigate methods in both physically based forward and inverse rendering that exploit light path gradients.

The first part is concerned with scattering from specular surfaces, which produces complex optical effects that are frequently encountered in realistic scenes: intricate caustics due to focused reflection, multiple refractions, and high-frequency glints from specular microstructure. Yet, despite their importance and considerable research to this end, sampling of light paths that cause these effects remains a formidable challenge of forward rendering.

We propose a surprisingly simple and general path sampling strategy that targets the examples above. Valid light path configurations need to fulfill the physical laws of reflection and refraction, and we find these using a numerical root-finding process that is driven by geometric light path gradients. In contrast to prior work, our method supports high-frequency normal- or displacement-mapped geometry, samples specular-diffuse-specular (SDS) paths, and is compatible with standard Monte Carlo methods including unidirectional path tracing. We demonstrate our method on a range of challenging scenes and evaluate it against state-of-the-art methods for rendering caustics and glints.

In the second part, we consider differentiable rendering algorithms. These propagate derivatives through the full light transport simulation to solve inverse rendering problems via gradient-based optimization. Recent progress has led to methods that can simultaneously compute derivatives with respect to millions of scene parameters. At the same time, elementary properties of these methods remain poorly understood.

Current algorithms for differentiable rendering are constructed by mechanically differentiating a given primal algorithm. As differentiation fundamentally changes the underlying problem, this is often suboptimal and instead, primal and differential algorithms should be decoupled so that the latter can suitably adapt. This is surprisingly complex. Even the most basic Monte Carlo path tracer already involves several design choices concerning the techniques for sampling materials and emitters, and their combination, e.g. via multiple importance sampling (MIS). Differentiation causes a veritable explosion of this decision tree: should we differentiate only the estimator, or also the sampling technique? Should MIS be applied before or after differentiation? Are specialized derivative sampling strategies of any use? How should visibility-related discontinuities be handled when millions of parameters are differentiated simultaneously? We provide a taxonomy and analysis of different estimators for differential light transport to provide intuition about these and related questions.