标题： MCMC：连接渲染、优化和生成式人工智能 显示英文标题

标题： MCMC: Bridging Rendering, Optimization and Generative AI

摘要： 生成式人工智能（AI）在过去两年中在视觉语言模型方面取得了前所未有的进展。 在生成过程中，从一个未知的高维分布中生成新的样本（图像）。 马尔可夫链蒙特卡洛（MCMC）方法在从这种复杂、高维分布中抽样时特别有效。 这使得MCMC方法成为EBM等模型的重要组成部分，确保准确的样本生成。 基于梯度的优化是现代生成模型的核心。 优化过程中的更新步骤形成一个马尔可夫链，其中新的更新仅依赖于当前状态。 这允许以无记忆的方式探索参数空间，从而结合基于梯度的优化和MCMC采样的优势。 在基于物理的渲染中，MCMC方法也表现出同样重要的作用，因为复杂的光路 otherwise 很难通过简单的重要性抽样技术进行抽样。 许多研究致力于以数据驱动的方式将物理真实性带入从扩散基生成模型生成的样本（图像），然而，连接这些技术的统一框架仍然缺失。 在本课程中，我们迈出第一步，以理解每个组件并探索MCMC如何可能作为桥梁，连接这些密切相关的研究领域。 我们的课程旨在为学生、研究人员和实践者提供必要的理论和实践工具，以实现生成式基于物理的渲染的共同目标。 所有与本教程相关的Jupyter笔记本均可在项目网页上找到：https://sinbag.github.io/mcmc/ 显示英文摘要

摘要： Generative artificial intelligence (AI) has made unprecedented advances in vision language models over the past two years. During the generative process, new samples (images) are generated from an unknown high-dimensional distribution. Markov Chain Monte Carlo (MCMC) methods are particularly effective in drawing samples from such complex, high-dimensional distributions. This makes MCMC methods an integral component for models like EBMs, ensuring accurate sample generation. Gradient-based optimization is at the core of modern generative models. The update step during the optimization forms a Markov chain where the new update depends only on the current state. This allows exploration of the parameter space in a memoryless manner, thus combining the benefits of gradient-based optimization and MCMC sampling. MCMC methods have shown an equally important role in physically based rendering where complex light paths are otherwise quite challenging to sample from simple importance sampling techniques. A lot of research is dedicated towards bringing physical realism to samples (images) generated from diffusion-based generative models in a data-driven manner, however, a unified framework connecting these techniques is still missing. In this course, we take the first steps toward understanding each of these components and exploring how MCMC could potentially serve as a bridge, linking these closely related areas of research. Our course aims to provide necessary theoretical and practical tools to guide students, researchers and practitioners towards the common goal of generative physically based rendering. All Jupyter notebooks with demonstrations associated to this tutorial can be found on the project webpage: https://sinbag.github.io/mcmc/