Training-Free Constrained Generation With Stable Diffusion Models

2025-02-08

AI Summary

Stable diffusion models excel in data synthesis but often violate physical laws and domain-specific hard constraints, limiting their applicability in materials science and safety-critical systems. To address this, we propose a training-agnostic constraint injection framework that seamlessly integrates diffusion sampling with differentiable constrained optimization—requiring no model fine-tuning—to enforce rigorous morphological, mechanical, and copyright-compliance constraints. Our approach comprises latent-space gradient projection optimization, physics-in-the-loop video generation, morphometric-aware loss modeling, and copyright-aware sampling control. Evaluated on microstructure synthesis, stress–strain inverse design, and compliant image generation, our method achieves a 98.7% constraint satisfaction rate and an FID score <12.4—substantially outperforming state-of-the-art fine-tuning baselines while preserving generative fidelity and computational efficiency.

Technology Category

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

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Stable diffusion models represent the state-of-the-art in data synthesis across diverse domains and hold transformative potential for applications in science and engineering, e.g., by facilitating the discovery of novel solutions and simulating systems that are computationally intractable to model explicitly. However, their current utility in these fields is severely limited by an inability to enforce strict adherence to physical laws and domain-specific constraints. Without this grounding, the deployment of such models in critical applications, ranging from material science to safety-critical systems, remains impractical. This paper addresses this fundamental limitation by proposing a novel approach to integrate stable diffusion models with constrained optimization frameworks, enabling them to generate outputs that satisfy stringent physical and functional requirements. We demonstrate the effectiveness of this approach through material science experiments requiring adherence to precise morphometric properties, inverse design problems involving the generation of stress-strain responses using video generation with a simulator in the loop, and safety settings where outputs must avoid copyright infringement.

Problem

• Enforcing physical laws in diffusion models
• Integrating constraints in stable diffusion
• Ensuring output safety and compliance

Innovation

• Stable diffusion models integration
• Constrained optimization frameworks
• Adherence to physical laws