Projected Coupled Diffusion for Test-Time Constrained Joint Generation

2025-08-14

AI Summary

This work addresses the weak inter-sample correlation and difficulty in satisfying task-specific constraints when jointly generating samples from multiple pre-trained diffusion models. We propose a test-time framework that synergistically combines coupling guidance with hard-constraint projection: a cross-model coupling guidance term is introduced during sampling, and differentiable constraint projection is applied after each denoising step—requiring no model retraining. To our knowledge, this is the first approach to unify coupling guidance and strict constraint satisfaction entirely at test time. The framework supports diverse tasks including image-pair generation, object manipulation, and multi-robot path planning. Experiments demonstrate substantial improvements in inter-model sample coherence, 100% satisfaction of geometric and kinematic hard constraints, low computational overhead, and consistent superiority over existing joint-generation and conditional diffusion methods across all evaluated metrics.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• Enforce constraints during joint generation without retraining
• Coordinate multiple diffusion models for correlated samples
• Achieve constraint satisfaction with low computational cost

Innovation

• Coupled guidance term for model coordination
• Projection step enforces hard constraints
• Test-time framework for joint generation