Training-Free Constrained Generation With Stable Diffusion Models

Stefano Zampini, Jacob K Christopher, Luca Oneto, Davide Anguita, Ferdinando Fioretto

Keywords: Stable Diffusion, Constrained Generation, Differentiable Optimization

TL;DR: By incorporating differentiable constraint evaluation functions directly into stable diffusion’s iterative sampling, this approach enforces physical and functional requirements in generative tasks.

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. While there is increasing effort to incorporate physics-based constraints into generative models, existing techniques are either limited in their applicability to latent diffusion frameworks or lack the capability to strictly enforce domain-specific constraints. To address this limitation this paper proposes a novel integration of stable diffusion models with constrained optimization frameworks, enabling the generation of outputs satisfying stringent physical and functional requirements. The effectiveness of this approach is demonstrated through material design experiments requiring adherence to precise morphometric properties, challenging inverse design tasks involving the generation of materials inducing specific stress-strain responses, and copyright-constrained content generation tasks. All code has been released at https://github.com/RAISELab-atUVA/Constrained-Stable-Diffusion.

Primary Area: Deep learning (e.g., architectures, generative models, optimization for deep networks, foundation models, LLMs)

Submission Number: 18436