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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2604.00327 |
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| _version_ | 1866911558763806720 |
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| author | Yasuda, Yuki Bischoff, Tobias |
| author_facet | Yasuda, Yuki Bischoff, Tobias |
| contents | Multiscale spatial structure complicates temporal prediction because small-scale spatial fluctuations influence large-scale evolution, yet resolving all scales is often intractable. Standard diffusion models do not address this problem effectively since they apply uniform decay across all Fourier modes. We propose Predictor-Driven Diffusion, a framework that combines renormalization-group-based spatial coarse-graining with a path-integral formulation of temporal dynamics. The forward process applies scale-dependent Laplacian damping together with additive noise, producing a hierarchy of coarse-grained fields indexed by diffusion scale $λ$. Training minimizes the Kullback-Leibler divergence between data-induced and predictor-induced path densities, leading to a simple regression loss on temporal derivatives. The resulting predictor captures how eliminated small-scale components statistically influence large-scale evolution. A key insight is that the same predictor provides a path score for reverse-$λ$ sampling, unifying simulation, unconditional generation, and super-resolution in a single framework. Our unified approach is validated through experiments on two multiscale turbulent systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00327 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Predictor-Driven Diffusion for Spatiotemporal Generation Yasuda, Yuki Bischoff, Tobias Fluid Dynamics Computational Physics Geophysics Multiscale spatial structure complicates temporal prediction because small-scale spatial fluctuations influence large-scale evolution, yet resolving all scales is often intractable. Standard diffusion models do not address this problem effectively since they apply uniform decay across all Fourier modes. We propose Predictor-Driven Diffusion, a framework that combines renormalization-group-based spatial coarse-graining with a path-integral formulation of temporal dynamics. The forward process applies scale-dependent Laplacian damping together with additive noise, producing a hierarchy of coarse-grained fields indexed by diffusion scale $λ$. Training minimizes the Kullback-Leibler divergence between data-induced and predictor-induced path densities, leading to a simple regression loss on temporal derivatives. The resulting predictor captures how eliminated small-scale components statistically influence large-scale evolution. A key insight is that the same predictor provides a path score for reverse-$λ$ sampling, unifying simulation, unconditional generation, and super-resolution in a single framework. Our unified approach is validated through experiments on two multiscale turbulent systems. |
| title | Predictor-Driven Diffusion for Spatiotemporal Generation |
| topic | Fluid Dynamics Computational Physics Geophysics |
| url | https://arxiv.org/abs/2604.00327 |