Langevin monte carlo rendering with gradient-based adaptation

We introduce a suite of Langevin Monte Carlo algorithms for efficient photorealistic rendering of scenes with complex light transport effects, such as caustics, interreflections, and occlusions. Our algorithms operate in primary sample space, and use the Metropolis-adjusted Langevin algorithm (MALA) to generate new samples. Drawing inspiration from state-of-the-art stochastic gradient descent procedures, we combine MALA with adaptive preconditioning and momentum schemes that re-use previously-computed first-order gradients, either in an online or in a cache-driven fashion. This combination allows MALA to adapt to the local geometry of the primary sample space, without the computational overhead associated with previous Hessian-based adaptation algorithms. We use the theory of controlled Markov chain Monte Carlo to ensure that these combinations remain ergodic, and are therefore suitable for unbiased Monte Carlo rendering. Through extensive experiments, we show that our algorithms, MALA with online and cache-driven adaptation, can successfully handle complex light transport in a large variety of scenes, leading to improved performance (on average more than 3× variance reduction at equal time, and 7× for motion blur) compared to state-of-the-art Markov chain Monte Carlo rendering algorithms.