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Jacob K Christopher

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NeurIPS Conference 2025 Conference Paper

Constrained Discrete Diffusion

Michael Cardei
Jacob K Christopher
Bhavya Kailkhura
Tom Hartvigsen
Ferdinando Fioretto

Discrete diffusion models are a class of generative models that construct sequences by progressively denoising samples from a categorical noise distribution. Beyond their rapidly growing ability to generate coherent natural language, these models present a new and important opportunity to enforce sequence-level constraints, a capability that current autoregressive models cannot natively provide. This paper capitalizes on this opportunity by introducing $\textit{Constrained Discrete Diffusion}$ (CDD), a novel integration of differentiable constraint optimization within the diffusion process to ensure adherence to constraints, logic rules, or safety requirements for generated sequences. Unlike conventional text generators that often rely on post-hoc filtering or model retraining for controllable generation, CDD directly imposes constraints into the discrete diffusion sampling process, resulting in a training-free and effective approach. Experiments in toxicity-controlled text generation, property-constrained molecule design, and instruction-constrained text completion demonstrate that CDD achieves $\textit{zero constraint violations}$ in a diverse array of tasks while preserving fluency, novelty, and coherence, and outperforming autoregressive and existing discrete diffusion approaches.

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NeurIPS Conference 2025 Conference Paper

Training-Free Constrained Generation With Stable Diffusion Models

Stefano Zampini
Jacob K Christopher
Luca Oneto
Davide Anguita
Ferdinando Fioretto

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.

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