Efficient Diffusion Models under Nonconvex Equality and Inequality constraints via Landing

2026-04-20

AI Summary

This work addresses the challenge of modeling feasible sets defined by non-convex equality and inequality constraints by proposing a unified constraint-preserving diffusion framework. The method simultaneously handles mixed constraints throughout the entire diffusion process, integrating both overdamped and underdamped dynamics to accelerate mixing with the prior distribution. It introduces a novel landing mechanism that guarantees constraint satisfaction without requiring iterative projections or Newton-type solvers. Experimental results demonstrate that the approach significantly reduces the number of function evaluations and memory overhead across multiple non-convex constrained benchmarks while achieving sample quality on par with state-of-the-art methods.

Technology Category

• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Non-convex Optimization
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.g., molecular generation, robotics). We present a unified framework for constrained diffusion models on generic nonconvex feasible sets $Σ$ that simultaneously enforces equality and inequality constraints throughout the diffusion process. Our framework incorporates both overdamped and underdamped dynamics for forward and backward sampling. A key algorithmic innovation is a computationally efficient landing mechanism that replaces costly and often ill-defined projections onto $Σ$, ensuring feasibility without iterative Newton solves or projection failures. By leveraging underdamped dynamics, we accelerate mixing toward the prior distribution, effectively alleviating the high simulation costs typically associated with constrained diffusion. Empirically, this approach reduces function evaluations and memory usage during both training and inference while preserving sample quality. On benchmarks featuring equality and mixed constraints, our method achieves comparable sample quality to state-of-the-art baselines while significantly reducing computational cost, providing a practical and scalable solution for diffusion on nonconvex feasible sets.

Problem

• constrained diffusion models
• nonconvex constraints
• equality and inequality constraints
• generative modeling
• feasible sets

Innovation

• constrained diffusion models
• nonconvex constraints
• landing mechanism
• underdamped dynamics
• projection-free sampling