Diffusion models have been successful on a range of conditional generation tasks including molecular design and text-to-image generation. However, these achievements have primarily depended on task-specific conditional training or error-prone heuristic approximations. Ideally, a conditional generation method should provide exact samples for a broad range of conditional distributions without requiring task-specific training. To this end, we introduce the Twisted Diffusion Sampler, or TDS. TDS is a sequential Monte Carlo (SMC) algorithm that targets the conditional distributions of diffusion models. The main idea is to use twisting, an SMC technique that enjoys good computational efficiency, to incorporate heuristic approximations without compromising asymptotic exactness. We first find in simulation and on MNIST image inpainting and class-conditional generation tasks that TDS provides a computational statistical trade-off, yielding more accurate approximations with many particles but with empirical improvements over heuristics with as few as two particles. We then turn to motif-scaffolding, a core task in protein design, using a TDS extension to Riemannian diffusion models. On benchmark test cases, TDS allows flexible conditioning criteria and often outperforms the state of the art.

翻译：扩散模型在分子设计、文本到图像生成等一系列条件生成任务中取得了成功。然而，这些成果主要依赖于任务特定的条件训练或易出错的启发式近似方法。理想情况下，条件生成方法应能为广泛的条件分布提供精确样本，且无需任务特定的训练。为此，我们提出了扭曲扩散采样器（Twisted Diffusion Sampler，简称TDS）。TDS是一种序贯蒙特卡洛（SMC）算法，专门针对扩散模型的条件分布进行采样。核心思想是利用扭曲技术——一种计算效率高的SMC方法——在保证渐近精确性的同时融入启发式近似。我们首先通过仿真实验以及MNIST图像修复和类别条件生成任务发现，TDS实现了计算与统计之间的权衡：使用大量粒子时可获得更精确的近似，而即便仅用两个粒子也能在经验上优于启发式方法。随后，我们将TDS扩展至黎曼扩散模型，并将其应用于蛋白质设计的核心任务——基序支架生成。在基准测试案例中，TDS支持灵活的条件约束标准，且性能通常优于现有最优方法。