Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation

Diffusion models show growing promise for generative modeling of physical systems, but enforcing partial differential equation (PDE) constraints directly is infeasible during the stochastic denoising process. Current methods apply constraints to the expected clean sample, incurring a Jensen's Gap that forces a trade-off between PDE satisfaction and generative accuracy. To bridge this gap, we propose Physics-Informed Distillation of Diffusion Models (PIDDM), a simple yet effective post-hoc distillation strategy that enforces PDE constraints after training. PIDDM enables fast single-step generation while improving both physical consistency and sample quality, supporting forward/inverse problems and reconstruction from partial observations. Extensive experiments across PDE benchmarks show PIDDM outperforms recent baselines, such as PIDM Bastek et al. [2025], DiffusionPDE Huang et al. [2024a], and ECI-sampling Cheng et al. [2025], in both accuracy and constraint satisfaction, with lower computation and minimal hyperparameter tuning, offering a more efficient pathway to physics-informed diffusion models.