Training-Free Constrained Generation With Stable Diffusion Models

Jacob K Christopher (University of Virginia) · Ferdinando Fioretto (University of Virginia) · Luca Oneto (University of Genoa) · Stefano Zampini (Polytechnic Institute of Turin) · Davide Anguita (University of Genoa)

computational intractability constrained optimizationcontent generationdata synthesisdomain-specific constraintsfunctional requirementsgenerative modelsinverse design taskslatent diffusion frameworksmaterial design experimentsmorphometric propertiesnovel solutionsphysics-based constraintsstable diffusion modelsstress-strain responses

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.