<ul><li>Researchers have introduced a new framework called FunDPS for conditional sampling in PDE-based inverse problems.</li><li>FunDPS aims to recover whole solutions from sparse or noisy measurements using a function-space diffusion model and plug-and-play conditioning.</li><li>The method involves training a denoising model with neural operator architectures and refining samples during inference to meet sparse observation data.</li><li>FunDPS demonstrates improved accuracy in capturing posterior distributions in function spaces with minimal supervision and data scarcity, making it a practical solution for PDE tasks.</li></ul>

Guided Diffusion Sampling on Function Spaces with Applications to PDEs

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