通过结构保持训练稳定求解偏微分方程的生成模型，大幅降低计算成本。
Stabilizing Physics-Informed Consistency Models via Structure-Preserving Training
- 分两阶段训练：先学数据分布，再冻结系数解码器强化物理约束
- 采用两步残差目标，提升生成轨迹的物理一致性与精度
- 零样本图像修复即可求解前向问题，推理速度比扩散模型快数个量级
我们提出一种基于物理约束的一致性建模框架，用于通过快速、少步生成推断求解偏微分方程（PDEs）。我们发现，在物理约束的一致性训练中，PDE残差可能使模型趋向平凡或退化解，破坏学习到的数据分布。为解决此问题，我们引入结构保持的两阶段训练策略，通过在物理约束微调阶段冻结系数解码器，实现分布学习与物理强制的解耦。进一步提出两步残差目标，在结构有效的生成轨迹上而非噪声单步预测上施加物理一致性。该框架实现了无条件生成和前向问题的稳定高保真推断。我们证明，前向解可通过基于投影的零样本图像修复过程获得，其一致性精度达到扩散基线水平，但计算成本降低数个数量级。
原文摘要 · Abstract (English)
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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