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arXiv · 2508.10531

Projected Coupled Diffusion for Test-Time Constrained Joint Generation

Hao Luan·Yi Xian Goh·See-Kiong Ng·Chun Kai Ling
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Abstract

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.

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Hao Luan, Yi Xian Goh, See-Kiong Ng, Chun Kai Ling. 2025-08-14. Projected Coupled Diffusion for Test-Time Constrained Joint Generation. https://arxiv.org/abs/2508.10531

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