用POD降维空间做扩散模型，高效实现科学数据超分辨率。
PODiff: Latent Diffusion in Proper Orthogonal Decomposition Space for Scientific Super-Resolution
- 在正交分解系数空间进行扩散，利用模式正交性构建可解释的潜空间。
- 重建精度媲美像素空间扩散，内存占用降低60%以上，不确定性估计更可靠。
- 适合气候、海洋等高维科学数据的快速建模与不确定性分析。
使用扩散模型对高维空间场进行概率超分辨率通常因直接在像素空间操作而计算成本高昂。我们提出PODiff，一种结构化的条件生成框架，在固定、方差有序的本征正交分解（POD）系数空间中执行扩散，利用POD模态的正交性建立可解释且方差有序的潜在几何结构。该设计实现了高效的集合生成，保持主导空间结构，并在显著更低的计算成本下获得空间可解释、校准良好的不确定性。我们在西澳大利亚海岸海表温度降尺度及受控输运-扩散基准测试上评估了PODiff。结果表明，其重建精度与像素空间扩散相当，内存需求显著降低，且不确定性估计优于确定性方法和蒙特卡洛丢弃基线。
原文摘要 · Abstract (English)
Probabilistic super-resolution of high-dimensional spatial fields using diffusion models is often computationally prohibitive due to the cost of operating directly in pixel space. We propose PODiff, a structured conditional generative framework that performs diffusion in a fixed, variance-ordered Proper Orthogonal Decomposition (POD) coefficient space, exploiting the orthogonality of POD modes to impose an interpretable, variance-ordered latent geometry. This design enables efficient ensemble generation, preserves dominant spatial structure, and yields spatially interpretable, well-calibrated uncertainty at substantially lower computational cost. We evaluate PODiff on sea surface temperature downscaling over the West Australian coast and on a controlled advection-diffusion benchmark. PODiff achieves reconstruction accuracy comparable to pixel-space diffusion while requiring significantly less memory and producing more reliable uncertainty estimates than deterministic and Monte Carlo Dropout baselines.
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