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This paper proposes a diffusion-based framework for learning adaptive mesh discretization conditioned on observed PDE dynamics, using spectral guidance and physics constraints to allocate resolution where needed. The method achieves competitive or superior performance across five PDE regimes.
Introduces Spectral Guidance, a framework for controlling diffusion models by leveraging low-dimensional representations of the diffusion process, enabling flexible and stable control without task-specific retraining or backpropagation through the denoiser.