# Uncertainty-Calibrated Spatiotemporal Field Diffusion with Sparse Supervision

Source: [Uncertainty-Calibrated Spatiotemporal Field Diffusion with Sparse Supervision](<https://www.sota2.com/research/paper/69aa5f7c2d603e6de3e4185e>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-03-07T05:00:04.447Z

Authors: Kevin Valencia, Xihaier Luo, Shinjae Yoo, David Keetae Park

Published: 2026-02-17T16:56:55.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Spatiotemporal Field Reconstruction on Navier-Stokes (Full)](<https://www.sota2.com/research/sota/spatiotemporal-field-reconstruction-on-navier-stokes-full.md>): Spatiotemporal Field Reconstruction; Navier-Stokes (Full); CRPS: 0.0968.

- [Spatiotemporal Field Reconstruction on Navier-Stokes 10% Subset](<https://www.sota2.com/research/sota/spatiotemporal-field-reconstruction-on-navier-stokes-10-percent-subset.md>): Spatiotemporal Field Reconstruction; Navier-Stokes 10% Subset; CRPS: 0.1005.

- [Spatiotemporal Forecasting on AirDelhi AD-B](<https://www.sota2.com/research/sota/spatiotemporal-forecasting-on-airdelhi-ad-b.md>): Spatiotemporal forecasting; AirDelhi AD-B; CRPS: 25.713.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2603.04431>)

[PDF](<https://arxiv.org/pdf/2603.04431.pdf>)