Langevin Monte Carlo Rendering with
Gradient-based Adaptation

Equal-time (20 minutes) comparison between MEMLT, MMLT, RJMLT, H2MC and two variants of our methods. The scene presents complex glossy and specular interreflections with difficult visibilities. The reference (Ref.) is rendered by BDPT in roughly a day. MEMLT suffers from correlated noise in the glass bottle region due to insufficient local exploration. MMLT and RJMLT both have severe noise because they sometimes get trapped in regions with hard-to-find features using Kelemen-style isotropic mutations. H2MC is more efficient with the help of anisotropic Gaussian mutations, but the computational overhead from Hessian computations and dense matrix operations results in a low sample budget and insufficient exploration. Our Langevin Monte Carlo methods efficiently address these challenges by exploiting first-order gradient information to robustly balance the tradeoff between adaptation and cost.


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.



We thank the anonymous SIGGRAPH reviewers for their valuable feedback. This work was supported by NSF grants 1730147, 1900783, 1900849, 1900927, and a gift from AWS Cloud Credits for Research.