Title: Accelerating Diffusion Models in Nonconvex Feasible Sets via Landing for Equality and Inequality Constraints

Abstract: In scientific and engineering domains where physical, geometric, or safety protocols must be strictly adhered to—such as in molecular design and robotics—generative modeling within constrained spaces is critical. This work introduces a comprehensive framework for diffusion models operating on general nonconvex feasible sets $\Sigma$, capable of handling both equality and inequality constraints throughout the entire diffusion trajectory. The proposed method integrates both overdamped and underdamped dynamics for forward and backward sampling phases. A central algorithmic contribution is the introduction of a computationally efficient "landing" mechanism, which substitutes expensive and frequently unstable projections onto $\Sigma$. This innovation guarantees constraint feasibility without relying on iterative Newton solvers or suffering from projection failures. Furthermore, by utilizing underdamped dynamics, the framework accelerates mixing toward the prior distribution, thereby mitigating the substantial simulation expenses usually linked to constrained diffusion. Empirical results demonstrate that this strategy lowers memory consumption and the number of function evaluations during both training and inference, all while maintaining high sample fidelity. Tests on benchmarks involving equality and mixed constraints reveal that our approach matches the sample quality of current state-of-the-art baselines while delivering a marked reduction in computational overhead, offering a practical and scalable solution for diffusion on nonconvex sets.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC