Strictly Constrained Generative Modeling via Split Augmented Langevin Sampling

• URL: http://arxiv.org/abs/2505.18017v2
• Date: Mon, 26 May 2025 02:13:32 GMT
• Title: Strictly Constrained Generative Modeling via Split Augmented Langevin Sampling
• Authors: Matthieu Blanke, Yongquan Qu, Sara Shamekh, Pierre Gentine,
• Abstract summary: We develop a principled framework for sampling from a target distribution while rigorously satisfying physical constraints.<n>We propose Split Augmented Langevin (SAL), a novel primal-dual sampling algorithm that enforces constraints progressively through variable splitting, with convergence guarantees.<n>We apply our method to diffusion-based data assimilation on a complex physical system, where enforcing physical constraints substantially improves both forecast accuracy and the preservation of critical conserved quantities.
• Score: 0.1052166918701117
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 physical constraints. Leveraging the variational formulation of Langevin dynamics, we propose Split Augmented Langevin (SAL), a novel primal-dual sampling algorithm that enforces constraints progressively through variable splitting, with convergence guarantees. While the method is developed theoretically for Langevin dynamics, we demonstrate its effective applicability to diffusion models. In particular, we use constrained diffusion models to generate physical fields satisfying energy and mass conservation laws. We apply our method to diffusion-based data assimilation on a complex physical system, where enforcing physical constraints substantially improves both forecast accuracy and the preservation of critical conserved quantities. We also demonstrate the potential of SAL for challenging feasibility problems in optimal control.

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