A Scale-Adaptive Framework for Joint Spatiotemporal Super-Resolution with Diffusion Models

Deep-learning video super-resolution has progressed rapidly, but climate applications typically super-resolve (increase resolution) either space or time, and joint spatiotemporal models are often designed for a single pair of super-resolution (SR) factors (upscaling spatial and temporal ratio between the low-resolution sequence and the high-resolution sequence), limiting transfer across spatial resolutions and temporal cadences (frame rates). We present a scale-adaptive framework that reuses the same architecture across factors by decomposing spatiotemporal SR into a deterministic prediction of the conditional mean, with attention, and a residual conditional diffusion model, with an optional mass-conservation (same precipitation amount in inputs and outputs) transform to preserve aggregated totals. Assuming that larger SR factors primarily increase underdetermination (hence required context and residual uncertainty) rather than changing the conditional-mean structure, scale adaptivity is achieved by retuning three factor-dependent hyperparameters before retraining: the diffusion noise schedule amplitude beta (larger for larger factors to increase diversity), the temporal context length L (set to maintain comparable attention horizons across cadences) and optionally a third, the mass-conservation function f (tapered to limit the amplification of extremes for large factors). Demonstrated on reanalysis precipitation over France (Comephore), the same architecture spans super-resolution factors from 1 to 25 in space and 1 to 6 in time, yielding a reusable architecture and tuning recipe for joint spatiotemporal super-resolution across scales.

Emulating Non-Differentiable Metrics via Knowledge-Guided Learning: Introducing the Minkowski Image Loss

The ``differentiability gap'' presents a primary bottleneck in Earth system deep learning: since models cannot be trained directly on non-differentiable scientific metrics and must rely on smooth proxies (e.g., MSE), they often fail to capture high-frequency details, yielding ``blurry'' outputs. We develop a framework that bridges this gap using two different methods to deal with non-differentiable functions: the first is to analytically approximate the original non-differentiable function into a differentiable equivalent one; the second is to learn differentiable surrogates for scientific functionals. We formulate the analytical approximation by relaxing discrete topological operations using temperature-controlled sigmoids and continuous logical operators. Conversely, our neural emulator uses Lipschitz-convolutional neural networks to stabilize gradient learning via: (1) spectral normalization to bound the Lipschitz constant; and (2) hard architectural constraints enforcing geometric principles. We demonstrate this framework's utility by developing the Minkowski image loss, a differentiable equivalent for the integral-geometric measures of surface precipitation fields (area, perimeter, connected components). Validated on the EUMETNET OPERA dataset, our constrained neural surrogate achieves high emulation accuracy, completely eliminating the geometric violations observed in unconstrained baselines. However, applying these differentiable surrogates to a deterministic super-resolution task reveals a fundamental trade-off: while strict Lipschitz regularization ensures optimization stability, it inherently over-smooths gradient signals, restricting the recovery of highly localized convective textures. This work highlights the necessity of coupling such topological constraints with stochastic generative architectures to achieve full morphological realism.