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DuoCast: Duo-Probabilistic Diffusion for Precipitation Nowcasting

Penghui Wen, Mengwei He, Patrick Filippi, Na Zhao, Feng Zhang, Thomas Francis Bishop, Zhiyong Wang, Kun Hu

TL;DR

DuoCast, a dual-diffusion framework that decomposes precipitation forecasting into low- and high-frequency components modeled in orthogonal latent subspaces, is proposed, theoretically proving that this frequency decomposition reduces prediction error compared to conventional single branch U-Net diffusion models.

Abstract

Accurate short-term precipitation forecasting is critical for weather-sensitive decision-making in agriculture, transportation, and disaster response. Existing deep learning approaches often struggle to balance global structural consistency with local detail preservation, especially under complex meteorological conditions. We propose DuoCast, a dual-diffusion framework that decomposes precipitation forecasting into low- and high-frequency components modeled in orthogonal latent subspaces. We theoretically prove that this frequency decomposition reduces prediction error compared to conventional single branch U-Net diffusion models. In DuoCast, the low-frequency model captures large-scale trends via convolutional encoders conditioned on weather front dynamics, while the high-frequency model refines fine-scale variability using a self-attention-based architecture. Experiments on four benchmark radar datasets show that DuoCast consistently outperforms state-of-the-art baselines, achieving superior accuracy in both spatial detail and temporal evolution.

DuoCast: Duo-Probabilistic Diffusion for Precipitation Nowcasting

TL;DR

DuoCast, a dual-diffusion framework that decomposes precipitation forecasting into low- and high-frequency components modeled in orthogonal latent subspaces, is proposed, theoretically proving that this frequency decomposition reduces prediction error compared to conventional single branch U-Net diffusion models.

Abstract

Accurate short-term precipitation forecasting is critical for weather-sensitive decision-making in agriculture, transportation, and disaster response. Existing deep learning approaches often struggle to balance global structural consistency with local detail preservation, especially under complex meteorological conditions. We propose DuoCast, a dual-diffusion framework that decomposes precipitation forecasting into low- and high-frequency components modeled in orthogonal latent subspaces. We theoretically prove that this frequency decomposition reduces prediction error compared to conventional single branch U-Net diffusion models. In DuoCast, the low-frequency model captures large-scale trends via convolutional encoders conditioned on weather front dynamics, while the high-frequency model refines fine-scale variability using a self-attention-based architecture. Experiments on four benchmark radar datasets show that DuoCast consistently outperforms state-of-the-art baselines, achieving superior accuracy in both spatial detail and temporal evolution.

Paper Structure

This paper contains 44 sections, 12 theorems, 33 equations, 11 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Precipitation Nowcasting
  4. Frequency Analysis and Modeling
  5. Methodology
  6. Problem Formulation
  7. Spectral Subspace Diffusion in DuoCast
  8. Low-Frequency Subspace Diffusion.
  9. High-Frequency Subspace Diffusion.
  10. Foundations of Spectral Subspace Diffusion
  11. Spectral Decay of Finite Support Convolutions.
  12. Sharp Tail Bound.
  13. Two–Stage Diffusion Modeling.
  14. Low-Frequency Diffusion Model
  15. Air Mass Spatial Modeling.
  16. ...and 29 more sections

Key Result

Lemma 1

Let $k \in L^{1}(\mathbb{R}^{d})$ be a convolution kernel with compact support and finite total variation, i.e. $k \in BV(\mathbb{R}^{d})$. Then there exists a constant $C_{\mathrm{BV}}>0$ (depending only on $\mathrm{TV}(k)$) such that

Figures (11)

  • Figure 1: Challenges in precipitation nowcasting: a) precipitation with weather (warm) front patterns, and b) high-frequency features (micro-scale variability) within edge regions shown in pink parallelograms.
  • Figure 2: Overview of DuoCast. A two-stage diffusion model leveraging historical weather fronts signals: (i) a low-frequency convolutional stage capturing front-guided precipitation trends, and (ii) a high-frequency self-attention stage refining micro-scale variability for pixel-level forecasts.
  • Figure 3: Qualitative comparison with SoTA on a SEVIR event. DuoCast captures finer micro-scale details (pink box) and preserves more consistent evolution trends (pink line).
  • Figure 4: Ablation study with qualitative SEVIR examples. (a) and (b) demonstrate the effectiveness of DuoCast in leveraging weather fronts, specifically cold and warm fronts, respectively. (c) highlights the capability of the high-frequency model in refining micro-scale variability. (d) showcases the impact of $\mathbf{Y^\dagger}$ for high-intensity regions prediction.
  • Figure 5: Visualization of air mass spatial modeling, highlighting captured weather fronts.
  • ...and 6 more figures

Theorems & Definitions (17)

  • Lemma 1: Polynomial Fourier decay of bounded variation (BV) kernels
  • Theorem 1: Spectral envelope under bounded variation
  • Theorem 2: Sharp capacity bottleneck
  • Corollary 1: Irreducible high‑frequency error
  • Corollary 2: Two–stage universal approximation
  • Lemma 2: Polynomial Fourier decay of bounded variation (BV) kernels
  • proof
  • Theorem 3: Spectral envelope under bounded variation
  • Lemma 3: Tail energy under BV envelope
  • proof
  • ...and 7 more