Uncertainty-Calibrated Spatiotemporal Field Diffusion with Sparse Supervision

• URL: http://arxiv.org/abs/2603.04431v1
• Date: Tue, 17 Feb 2026 16:56:55 GMT
• Title: Uncertainty-Calibrated Spatiotemporal Field Diffusion with Sparse Supervision
• Abstract summary: We present SOLID, a mask-conditioned diffusion framework that learns from sparse observations alone.<n>Training and evaluation use only observed target locations, requiring no dense fields and no pre-imputation.
• Score: 15.213950046367538
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Physical fields are typically observed only at sparse, time-varying sensor locations, making forecasting and reconstruction ill-posed and uncertainty-critical. We present SOLID, a mask-conditioned diffusion framework that learns spatiotemporal dynamics from sparse observations alone: training and evaluation use only observed target locations, requiring no dense fields and no pre-imputation. Unlike prior work that trains on dense reanalysis or simulations and only tests under sparsity, SOLID is trained end-to-end with sparse supervision only. SOLID conditions each denoising step on the measured values and their locations, and introduces a dual-masking objective that (i) emphasizes learning in unobserved void regions while (ii) upweights overlap pixels where inputs and targets provide the most reliable anchors. This strict sparse-conditioning pathway enables posterior sampling of full fields consistent with the measurements, achieving up to an order-of-magnitude improvement in probabilistic error and yielding calibrated uncertainty maps (\r{ho} > 0.7) under severe sparsity.

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