Multiphase-Diff：面向具有尖锐界面的高对比度多相物理系统的基于扩散的生成建模
Multiphase-Diff: Diffusion-Based Generative Modeling for High-Contrast Multiphase Physical Systems with Sharp Interfaces
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中文总结 AI 辅助
针对高对比度多相物理系统的扩散生成建模难题，提出Multiphase-Diff方法，通过三项改进实现更优的物理与分布保真度，在多相基准上优于7个基线模型，适用于该场景的科学样本生成。
中文摘要 AI 辅助
物理约束扩散在处理高对比度、尖锐界面的多相场时面临三个耦合难题：在系数跃变处，扩展的逐点强形式偏微分方程残差包含奇异梯度项，可能对物理界面造成惩罚；在极端对比度下，低幅值相可能低于扩散噪声基底，被擦除、错定尺度或生成负系数，而全局似然尺度会让高幅值相主导监督。为此，本文提出Multiphase-Diff，对应作出三项贡献：(i) 保守通量残差，避免对不连续系数求导并强制离散守恒；(ii) 解析双射表示，将低幅值信号映射到一阶潜变量尺度，通过指数解码保证系数为正；(iii) 雅可比预处理似然，归一化局部残差尺度以实现均衡监督。在三个互补的多相基准上开展的实验表明，Multiphase-Diff在物理保真度和分布保真度上均优于7个基线模型，且在相对比度和组成上具有鲁棒性，确立了其在该具挑战性的场景下用于科学样本生成的有效性。
英文摘要
Physics-constrained diffusion for high-contrast, sharp-interface multiphase fields faces three coupled difficulties. At coefficient jumps, expanded pointwise strong-form PDE residuals contain singular gradient terms that can penalize physical interfaces. Under extreme contrast, low-magnitude phases may fall below the diffusion noise floor and be erased, misscaled, or generated with negative coefficients, while a global likelihood scale allows high-magnitude phases to dominate supervision. We therefore propose Multiphase-Diff, which makes three corresponding contributions: (i) a conservative flux residual that avoids differentiating discontinuous coefficients and enforces discrete conservation; (ii) an analytic bijective representation that maps low-amplitude signals to order-one latent scales and guarantees coefficient positivity through exponential decoding; and (iii) a Jacobi-preconditioned likelihood that normalizes local residual scales for balanced supervision. Experiments on three complementary multiphase benchmarks demonstrate the superiority of Multiphase-Diff over seven baselines in both physical and distributional fidelity and its robustness across phase contrasts and compositions, establishing its effectiveness for scientific sample generation in this challenging regime.
