[2505.18017] Strictly Constrained Generative Modeling via Split Augmented Langevin Sampling

Computer Science > Machine Learning arXiv:2505.18017 (cs) [Submitted on 23 May 2025 (v1), last revised 2 Mar 2026 (this version, v3)] Title:Strictly Constrained Generative Modeling via Split Augmented Langevin Sampling Authors:Matthieu Blanke, Yongquan Qu, Sara Shamekh, Pierre Gentine View a PDF of the paper titled Strictly Constrained Generative Modeling via Split Augmented Langevin Sampling, by Matthieu Blanke and 3 other authors View PDF HTML (experimental) Abstract:Deep generative models hold great promise for representing complex physical systems, but their deployment is currently limited by the lack of guarantees on the physical plausibility of the generated outputs. Ensuring that known physical constraints are enforced is therefore critical when applying generative models to scientific and engineering problems. We address this limitation by developing a principled framework for sampling from a target distribution while rigorously satisfying mathematical constraints. Leveraging the variational formulation of Langevin dynamics and Lagrangian duality, we propose Constrained Alternated Split Augmented Langevin (CASAL), a novel primal-dual sampling algorithm that enforces constraints progressively through variable splitting. We analyze our algorithm in Wasserstein space and derive explicit mixing time rates. While the method is developed theoretically for Langevin dynamics, we demonstrate its applicability to diffusion models. We apply our method to diffusion-based data ...