Constraint-Guided Prediction Refinement via Deterministic Diffusion Trajectories

2025/06/15 by Pantelis Dogoulis, Dogoulis, Pantelis, Fabien Bernier +7
Computer Science · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning and Data Classification #Natural Language Processing Techniques

paper · pdf · doi:10.48550/arxiv.2506.12911

openalex publication_date 2025/06/15 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

Many real-world machine learning tasks require outputs that satisfy hard constraints, such as physical conservation laws, structured dependencies in graphs, or column-level relationships in tabular data. Existing approaches rely either on domain-specific architectures and losses or on strong assumptions on the constraint space, restricting their applicability to linear or convex constraints. We propose a general-purpose framework for constraint-aware refinement that leverages denoising diffusion implicit models (DDIMs). Starting from a coarse prediction, our method iteratively refines it through a deterministic diffusion trajectory guided by a learned prior and augmented by constraint gradient corrections. The approach accommodates a wide class of non-convex and nonlinear equality constraints and can be applied post hoc to any base model. We demonstrate the method in two representative domains: constrained adversarial attack generation on tabular data with column-level dependencies and in AC power flow prediction under Kirchhoff's laws. Across both settings, our diffusion-guided refinement improves both constraint satisfaction and performance while remaining lightweight and model-agnostic.

Citations

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• Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow
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Related

• Integration Matters: Rollout-Based Training for Constrained Diffusion Models
• Physics-Informed Diffusion Models
• Diffusion models as plug-and-play priors
• Constraint-Aware Diffusion Models for Trajectory Optimization
• Mirror Diffusion Models for Constrained and Watermarked Generation