Stabilizing Physics-Informed Consistency Models via Structure-Preserving Training

• URL: http://arxiv.org/abs/2602.09303v1
• Date: Tue, 10 Feb 2026 00:40:19 GMT
• Title: Stabilizing Physics-Informed Consistency Models via Structure-Preserving Training
• Authors: Che-Chia Chang, Chen-Yang Dai, Te-Sheng Lin, Ming-Chih Lai, Chieh-Hsin Lai,
• Abstract summary: We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs)<n>We identify a key stability challenge in physics-constrained consistency training, where PDE residuals can drive the model toward trivial or degenerate solutions.<n>We introduce a structure-preserving two-stage training strategy that decouples distribution learning from physics enforcement.
• Score: 7.031010831953522
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs) via fast, few-step generative inference. We identify a key stability challenge in physics-constrained consistency training, where PDE residuals can drive the model toward trivial or degenerate solutions, degrading the learned data distribution. To address this, we introduce a structure-preserving two-stage training strategy that decouples distribution learning from physics enforcement by freezing the coefficient decoder during physics-informed fine-tuning. We further propose a two-step residual objective that enforces physical consistency on refined, structurally valid generative trajectories rather than noisy single-step predictions. The resulting framework enables stable, high-fidelity inference for both unconditional generation and forward problems. We demonstrate that forward solutions can be obtained via a projection-based zero-shot inpainting procedure, achieving consistent accuracy of diffusion baselines with orders of magnitude reduction in computational cost.

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