Multiphase-Diff: Diffusion-Based Generative Modeling for High-Contrast Multiphase Physical Systems with Sharp Interfaces

Researchers propose Multiphase-Diff, a diffusion-based generative model for high-contrast multiphase physical systems with sharp interfaces, addressing three coupled difficulties: singular gradient terms at coefficient jumps, low-magnitude phases falling below the noise floor, and global likelihood scale dominance. The model introduces a conservative flux residual, an analytic bijective representation, and a Jacobi-preconditioned likelihood. Experiments on three multiphase benchmarks show Multiphase-Diff outperforms seven baselines in physical and distributional fidelity, demonstrating robustness across phase contrasts and compositions.

arXiv:2608.13669v1 Announce Type: new Abstract: 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.