标题： 测试时间约束联合生成的投影耦合扩散 显示英文标题

标题： Projected Coupled Diffusion for Test-Time Constrained Joint Generation

摘要： 对测试时采样的修改已成为扩散算法的重要扩展，其目标是在不重新训练整个扩散模型的情况下，使生成过程偏向于实现给定的目标。 然而，在不进行昂贵的重新训练的情况下，从多个预训练的扩散模型中联合生成相关样本，并同时执行特定任务的约束仍然具有挑战性。 为此，我们提出了投影耦合扩散（PCD），这是一种用于约束联合生成的新测试时框架。 PCD在生成动力学中引入了一个耦合引导项，以促进扩散模型之间的协调，并在每个扩散步骤中引入一个投影步骤以强制执行硬约束。 实证上，我们在图像对生成、物体操作和多机器人运动规划的应用场景中展示了PCD的有效性。 我们的结果表明，在不产生过多计算成本的情况下，实现了改进的耦合效果和保证的约束满足。 显示英文摘要

摘要： Modifications to test-time sampling have emerged as an important extension to diffusion algorithms, with the goal of biasing the generative process to achieve a given objective without having to retrain the entire diffusion model. However, generating jointly correlated samples from multiple pre-trained diffusion models while simultaneously enforcing task-specific constraints without costly retraining has remained challenging. To this end, we propose Projected Coupled Diffusion (PCD), a novel test-time framework for constrained joint generation. PCD introduces a coupled guidance term into the generative dynamics to encourage coordination between diffusion models and incorporates a projection step at each diffusion step to enforce hard constraints. Empirically, we demonstrate the effectiveness of PCD in application scenarios of image-pair generation, object manipulation, and multi-robot motion planning. Our results show improved coupling effects and guaranteed constraint satisfaction without incurring excessive computational costs.