Markov chain Monte Carlo (MCMC) algorithms come to rescue when sampling from a complex, high-dimensional distribution by a conventional method is intractable. Even though MCMC is a powerful tool, it is also hard to control and tune in practice. Simultaneously achieving both local exploration of the state space and global discovery of the target distribution is a challenging task. In this work, we present a MCMC formulation that subsumes all existing MCMC samplers employed in rendering. We then present a novel framework for adjusting an arbitrary Markov chain, making it exhibit invariance with respect to a specified target distribution. To showcase the potential of the proposed framework, we focus on a first simple application in light transport simulation. As a by-product, we introduce continuous-time MCMC sampling to the computer graphics community. We show how any existing MCMC-based light transport algorithm can be embedded into our framework. We empirically and theoretically prove that this embedding is superior to running the standalone algorithm. In fact, our approach will convert any existing algorithm into a highly parallelizable variant with shorter running time, smaller error and less variance.

翻译：当从复杂的高维分布中采样时，若传统方法难以处理，马尔可夫链蒙特卡洛（MCMC）算法便成为有效的解决工具。尽管MCMC是一种强大的方法，但在实践中其控制和调优也颇具挑战。同时实现状态空间的局部探索与目标分布的全局发现是一项艰巨的任务。在本研究中，我们提出了一种MCMC框架，该框架涵盖了渲染领域所有现有的MCMC采样器。随后，我们提出了一种新颖的框架，用于调整任意马尔可夫链，使其对指定的目标分布表现出不变性。为展示所提框架的潜力，我们聚焦于光传输模拟中的首个简单应用。作为副产品，我们将连续时间MCMC采样引入计算机图形学界。我们展示了如何将任何现有的基于MCMC的光传输算法嵌入到我们的框架中。我们通过实证与理论证明，这种嵌入优于独立运行原算法。事实上，我们的方法能够将任何现有算法转换为具有更短运行时间、更小误差和更低方差的高度可并行化变体。