Consistency Training with Physical Constraints

We propose a physics-aware Consistency Training (CT) (Song et al., 2023) method that accelerates sampling in Diffusion Models with physical constraints. Experiments on toy examples show that our method generates samples in a single step while adhering to the imposed constraints. This approach has the potential to efficiently solve partial differential equations (PDEs) using deep generative modeling. Diffusion models (Sohl-Dickstein et al., 2015; Song & Ermon, 2019; Ho et al., 2020; Song et al., 2021b) have achieved significant success in high-dimensional data generation. Recent efforts have focused on adapting diffusion models to generate samples that satisfy physical constraints (Yuan et al., 2023; Mazé & Ahmed, 2023; Shu et al., 2023; Jacobsen et al., 2024; Bastek et al., 2024).