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.
@article{arxiv.2508.10531,
title = {Projected Coupled Diffusion for Test-Time Constrained Joint Generation},
author = {Hao Luan and Yi Xian Goh and See-Kiong Ng and Chun Kai Ling},
journal= {arXiv preprint arXiv:2508.10531},
year = {2026}
}