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

2026-08-13

AI Summary

This study addresses gradient singularities, signal annihilation, and supervision imbalance in high-contrast multiphase field diffusion generation by proposing a physics-constrained diffusion framework. The approach employs conservative flux residuals to circumvent differential discontinuities, utilizes analytical bijective representations to ensure positivity and prevent low-amplitude phase loss, and incorporates Jacobi-preconditioned likelihood to resolve scale imbalances. Evaluated across three benchmarks, the proposed method significantly outperforms seven baselines, effectively enhancing both physical consistency and distributional fidelity. Furthermore, it demonstrates strong robustness under varying phase contrasts and compositional conditions, enabling the generation of high-fidelity scientific samples for complex multiphase systems.

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.

Problem

• Multiphase physical systems
• Sharp interfaces
• High-contrast
• Physics-constrained diffusion
• Generative modeling

Innovation

• Conservative Flux Residual
• Analytic Bijective Representation
• Jacobi-Preconditioned Likelihood
• Physics-Constrained Diffusion
• Multiphase Systems