The absence of real-world ground truth (GT) remains a challenge in multi-exposure image fusion (MEF). Benchmarks synthesizing pseudo GT through algorithm ensembles. Existing methods, hampered by inherent imperfections of pseudo GT and fixed mapping relationships, show limited performance and robustness. To address the limitations, we propose a novel cross-modal diffusion framework that synergizes text prompts and semantic perception for MEF, termed as Diff-MEF. First, it reformulates MEF as a probabilistic estimation task with conditional diffusion model for progressive transition and fusion. Then, we explicitly infer semantic and exposure priors as text prompts and semantic perception to improve performance and robustness. The priors are synergized through multi-modal prior embedding and optimization guidance. On the one hand, regarding cross-modal interaction, multi-modal priors, including segmentation masks, and exposure- and content-aware text prompts, are embedded into diffusion process by dedicated encoders and refine visual features through a text-segmentation refinement module. On the other hand, a semantic-level contrastive loss builds a regularization between cross-modal features in the semantic space of CLIP to mitigate degradations introduced by pseudo GT and fusion distortions. Experiments demonstrate that Diff-MEF outperforms SOTA methods and pseudo GT with superior fusion performance and robustness across diverse exposure scenarios. Code is available at https://github.com/hanna-xu/Diff-MEF.

Neural PDE surrogates can improve the cost-accuracy tradeoff of classical solvers, but often generalize poorly to new initial conditions and accumulate errors over time. Physical and symmetry constraints have shown promise in closing this performance gap, but existing techniques for imposing these inductive biases are incompatible with the staggered grids commonly used in computational fluid dynamics. Here we introduce novel input and output layers that respect physical laws and symmetries on the staggered grids, and for the first time systematically investigate how these constraints, individually and in combination, affect the accuracy of PDE surrogates. We focus on two challenging problems: shallow water equations with closed boundaries and decaying incompressible turbulence. Compared to strong baselines, symmetries and physical constraints consistently improve performance across tasks, architectures, autoregressive prediction steps, accuracy measures, and network sizes. Symmetries are more effective than physical constraints, but surrogates with both performed best, even compared to baselines with data augmentation or pushforward training, while themselves benefiting from the pushforward trick. Doubly-constrained surrogates also generalize better to initial conditions and durations beyond the range of the training data, and more accurately predict real-world ocean currents.