Stabilizing Physics-Informed Consistency Models via Structure-Preserving Training

TL;DR

This paper introduces a structure-preserving training method for physics-informed consistency models that stabilizes PDE solutions, enabling fast, accurate, and computationally efficient generative inference.

Contribution

It proposes a two-stage training strategy and residual objective to improve stability and physical consistency in PDE modeling, addressing key challenges in physics-constrained generative models.

Findings

Achieves stable, high-fidelity PDE solutions with fewer inference steps.

Reduces computational cost by orders of magnitude compared to diffusion baselines.

Enables zero-shot inpainting for forward PDE problems.

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.