PaperlayerView exact revision on arXiv

Source-linked AI summary

Diffusion-Based Rollouts as a Stabilization Mechanism for Long-Horizon Environmental Forecasting

Marina Vicens-Miquel, Amy McGovern, Aaron J. Hill, Efi Foufoula-Georgiou, Samuel S. P. Shen

arXiv:2609.33930v1cs.LGcs.AI

TL;DR

Long-horizon environmental forecasting must extend lead times while maintaining predictive skill, but recursive forecasts accumulate error and diffusion’s role in controlling that growth is not well understood. This paper compares matched diffusion and deterministic rollouts for water-level series and precipitation fields, finding that diffusion moderates recursive error growth while its practical value depends on both instability and available predictive information.

  • Problem

    Recursive forecasting extends environmental lead times but accumulated errors can degrade long-horizon skill, and diffusion’s behavior under repeated recursive application remains less understood.

    Source: §1 · p. 2

  • Method

    The study compares deterministic and diffusion-based recursive forecasts across water-level time series and precipitation fields using matched predictive backbones within each modality.

    Source: §1 · p. 3, §3 · p. 5

  • Results

    Diffusion moderates recursive error growth, with precipitation rollouts retaining HRRR guidance better preserving spatial organization and event-detection skill, while water-level fidelity can decline as external predictive information is lost.

    Source: §1 · p. 3, §5 · p. 14

  • Takeaways & Limitations

    The practical benefit of diffusion depends on recursive instability and the predictive information available, so rollout stability and forecast fidelity should be evaluated separately.

    Source: §5 · p. 14

    Water-level rollouts use only current and lagged observations and cannot recover future changes driven by external forcing absent from their inputs.

    Source: §4.1 · p. 8, §5 · p. 14

Abstract

from arXiv · show

Extending forecast lead times while maintaining predictive skill remains a major challenge in environmental forecasting. We investigate diffusion-based rollouts as a stabilization mechanism for recursive forecasting using low-dimensional water-level time series and high-dimensional precipitation fields. Across both modalities, diffusion suppresses recursive error growth, with the largest stabilization occurring where deterministic rollouts are most unstable. However, stabilization does not guarantee forecast fidelity. In the water-level experiments, forecasts progressively lose event-level fidelity as the rollout loses access to external predictive information, and trajectory-level comparisons show that diffusion can remain numerically stable while contracting toward central values and exhibiting reduced variability. In the precipitation experiments, which retain conditioning from numerical weather prediction throughout the rollout, diffusion better preserves spatial organization and event-detection skill. Together, these contrasting experiments indicate that diffusion can control recursive error amplification, while its practical benefit also depends on the predictive information available to constrain future evolution.

1 Introduction

Long-horizon environmental rollouts extend short-term forecasts but accumulate error, while diffusion’s role in controlling that growth during recursive forecasting is less understood. The paper compares matched deterministic and diffusion rollouts and finds stabilization is regime-dependent, with forecast fidelity needing separate evaluation.

1 Introduction

  • Recursive forecasting extends short-term predictions by feeding them back as inputs, but accumulated errors and uncertainty can degrade skill at longer horizons.Nonlinear and chaotic environmental dynamics can amplify small perturbations across spatial and temporal scales.Source: §1 · p. 2
  • Diffusion models sample learned conditional distributions through iterative denoising, but their behavior under repeated recursive application and their ability to control long-horizon error growth remain less understood.Prior rollout-stability approaches have focused more on architecture or training procedures than on modeling uncertainty within recursion.Source: §1 · p. 3
  • The study compares diffusion and deterministic autoregressive rollouts across water-level time series and precipitation fields using matched architectures, datasets, and normalization within each modality.This design separates the effects of diffusion-based recursive prediction from architectural and data-driven differences.Source: §1 · p. 3
  • Diffusion moderates recursive error growth across forecasting regimes, but its practical effects vary with instability and the predictive information available during rollout.Water-level rollouts can remain numerically bounded while losing event-level fidelity; precipitation rollouts with external forecast guidance better preserve spatial organization and event-detection skill.Source: §1 · p. 3
  • The paper frames diffusion as a stabilization tool rather than a uniform accuracy enhancer and argues that rollout stability and forecast fidelity should be evaluated separately.Numerical stabilization can coexist with retained predictive structure or with progressive loss of variability and event-level information.Source: §1 · pp. 3–4

2 Datasets

The experiments compare recursive forecasting in low-dimensional water-level series and high-dimensional precipitation fields, which differ in external predictive conditioning. The datasets and inputs establish these contrasting settings, including water-level-history-only forecasts and precipitation forecasts that retain HRRR guidance.

2 Datasets

  • Experiments use low-dimensional water-level time series and high-dimensional raster precipitation data to evaluate rollouts under differing degrees of external predictive conditioning.The two modalities provide contrasting environmental forecasting settings.Source: §2 · p. 4

2.1 Low-Dimensional Tabular Time Series

  • The tabular datasets comprise cleaned, gap-filled NOAA water levels at six-minute resolution from Bob Hall Pier, Rockport, and Port Isabel, three Texas Gulf Coast stations with distinct variability and predictability.The station differences reflect coastal geometry and environmental forcing.Source: §2.1 · p. 4

2.1.1 Target and Inputs

  • Both tabular models predict surge 12 hours ahead from current and lagged surge observations, excluding wind inputs to avoid unrealistically perfect future forcing during recursive rollouts.Surge is observed water level minus harmonic tidal prediction; predicted surge is combined with the tidal component to reconstruct total water level.Source: §2.1.1 · p. 4

2.2 High-Dimensional Raster Data

  • The raster experiments use 512×512 grids at 1 km resolution across regions centered on Oklahoma, Washington, D.C., and Oregon, with data spanning March 2021 through February 2025.The regions represent diverse precipitation regimes and geographic influences across CONUS.Source: §2.2 · p. 4

2.2.1 Target and Inputs

  • Raster models predict the one-hour precipitation residual relative to HRRR using MRMS observations, HRRR forecasts, geographic coordinates, and cyclical time encodings.HRRR forecasts are interpolated from 3 km to the 1 km MRMS grid, providing externally generated forecast information that can advance through the rollout.Source: §2.2.1 · p. 5

3 Methodology

The methodology compares deterministic and diffusion-based recursive forecasts using matched backbones, inputs, and rollout structures. It evaluates water-level and precipitation forecasts, with external forecast conditioning retained only in the raster setting.

3 Methodology

  • Both modalities compare deterministic and diffusion forecasts with the same backbone, input data, and recursive structure; diffusion adds noise-conditioned training and iterative denoising.EDM generates predictions by progressively denoising an initially noisy state across decreasing noise levels.Source: §3 · p. 5, §3.2 · p. 6

3.1 Forecasting Setup and Rollouts

  • Raster rollouts advance precipitation inputs and HRRR conditioning fields together, retaining external forecast information throughout recursion; tabular rollouts become fully autoregressive as observed surge values are replaced by predictions.In the raster setting, HRRR fields advance in forecast lead time alongside the precipitation inputs.Source: §3.1 · p. 5

3.2.1 Low-Dimensional Configuration

  • For water levels, the tabular diffusion model uses the MLP backbone with EDM x0 prediction and a hybrid loss combining noise-scaled reconstruction with conventional MSE.The noise-scaled term emphasizes reconstruction at lower noise levels; α = 0.8 controls the relative contribution of the two loss components.Source: §3.2.1 · p. 6

3.2.2 High-Dimensional Configuration

  • For precipitation, the diffusion model uses a dilated attention U-Net to predict clean residuals with EDM preconditioning, while its deterministic counterpart predicts residuals directly.Diffusion inference uses a single stochastic realization without ensemble averaging; training objectives combine noise-scaled MAE with percentile-based intensity weighting.Source: §3.2.2 · pp. 6–7

3.3 Evaluation Metrics

  • Evaluation uses water-level MAE for tabular forecasts and precipitation MAE, neighborhood-based FSS, and grid-cell CSI for raster forecasts.FSS assesses spatial agreement using 27 × 27 neighborhoods, while CSI assesses event-detection skill at individual grid cells.Source: §3.3 · pp. 7–8

4 Results and Discussion

Diffusion rollouts slow error growth across water-level and precipitation forecasts, with larger relative stabilization where deterministic rollouts degrade more. Their practical value differs by setting: water-level forecasts lose event fidelity as predictive information runs out, while HRRR-conditioned precipitation forecasts better preserve spatial structure and event-detection skill.

4.1 Tabular Rollout Evaluation

  • At longer lead times, diffusion increasingly reduces MAE relative to the deterministic MLP, with the largest gain at Rockport and the smallest at Bob Hall Pier.Diffusion has little advantage and can slightly increase MAE at the shortest lead times; it degrades more slowly than the deterministic MLP relative to the 12-hour forecast at all three stations.Source: §4.1 · p. 8, Figure 1 · p. 9
  • Larger deterministic error growth corresponds to larger relative diffusion improvements, but water-level forecasts still lose event-level fidelity, especially at Port Isabel and Rockport.Bob Hall Pier retains the greatest correspondence with observations; at Rockport, diffusion remains more numerically bounded while both approaches lose realistic event evolution.Source: §4.1 · p. 8, Figure 2 · p. 10

4.2 Raster Rollout Evaluation

  • Diffusion gains in Washington, D.C. and Oregon are clearest in FSS and CSI, while Oklahoma shows little MAE improvement; diffusion generally slows degradation, especially where deterministic structural skill deteriorates rapidly.The Oregon example shows broader, less coherent features in deterministic forecasts and greater spatial organization in diffusion forecasts.Source: §4.2 · p. 11
  • Water-level rollouts eventually rely only on prior model predictions, whereas precipitation rollouts retain advancing HRRR forecasts; diffusion cannot recover predictive information absent from the inputs.The contrast helps explain why stabilization accompanies better spatial structure and event-detection skill in precipitation, but can coexist with lost event information in water-level forecasts.Source: §4.1 · p. 8, §4.2 · p. 11

5 Conclusions

The study evaluates diffusion rollouts as a means of stabilizing recursive forecasts of water levels and precipitation. Diffusion moderates error growth in both settings, but its practical benefit depends on the predictive information available during rollout, with precipitation structure better preserved under continuing HRRR conditioning.

5 Conclusions

  • Across water-level and precipitation forecasts, diffusion moderates recursive error growth, but the magnitude and practical value of stabilization vary across forecasting regimes.The representative forecasts contrast Oregon precipitation spatial structure with progressive variability loss in Bob Hall Pier water-level forecasts.Source: §5 · p. 11, Figure 3 · p. 12
  • Water-level forecasts use only current and lagged levels and progressively lose independent predictive information; diffusion cannot recover future evolution driven by absent external forcing.Bob Hall Pier remains comparatively stable, Port Isabel loses event amplitude, and Rockport loses substantial event-level fidelity.Source: §5 · p. 14
  • With advancing HRRR forecasts conditioning precipitation rollouts, diffusion stabilization is associated with better preservation of coherent structure and event-detection skill, particularly where deterministic rollouts degrade rapidly.The raster figure compares diffusion and deterministic U-Net performance across three regions and lead times.Source: Figure 4 · p. 13, §5 · p. 14
  • Long-horizon forecasts face both recursive error amplification and loss of predictive information, so rollout stability and forecast fidelity should be evaluated separately.The practical benefit of diffusion depends on both recursive degradation and information available to constrain future evolution.Source: §5 · p. 14

Appendix A Appendix A: Dataset Splits

Appendix A describes the tide-gauge dataset splits, listing training, validation, and testing years for each station.

Appendix A: Dataset Splits

  • Table A1 lists the training, validation, and testing years for each NOAA tide-gauge station.The five-year station datasets use the three oldest years for training, the fourth for validation, and the final year for testing.Source: Table A1 · p. 14, Appendix A · p. 14

Appendix B Appendix B: Diffusion Hyperparameters

The diffusion framework and MLP backbone are shared across tide gauges, while selected diffusion hyperparameters are specified by station. Table B1 summarizes the station-specific settings.

Appendix B: Diffusion Hyperparameters

  • The diffusion framework and MLP backbone are consistent across stations, but selected diffusion hyperparameters vary by location.Source: Appendix B · p. 14
  • Pmean and Pstd set the mean and standard deviation of the log-normal distribution used to sample training noise levels.σdata is the assumed standard deviation of clean training data for EDM preconditioning; pdet is an additional tabular-diffusion training hyperparameter.Source: Appendix B · p. 14
  • Table B1 summarizes the diffusion hyperparameters used for each tide gauge location.The diffusion framework and MLP backbone remain consistent across locations, with selected hyperparameters specified separately by station.Source: Appendix B · p. 14, Table B1 · p. 15

Appendix C Appendix C: Raster Forecasting Architecture

Raster forecasting uses a dilated attention U-Net predictive backbone. The diffusion configuration embeds that backbone within the EDM framework.

Appendix C: Raster Forecasting Architecture

Appendix D Appendix D: Additional Visual Examples

Additional examples contrast precipitation structure and water-level event fidelity as lead time increases. The outcomes differ across regions and stations.

Appendix D: Additional Visual Examples

  • In Washington, D.C., diffusion retains greater spatial organization with increasing lead time, while deterministic precipitation features become broader and smoother.The raster examples complement quantitative MAE, FSS, and CSI results by showing precipitation structure as lead time increases.Source: Appendix D · p. 15, Figure D1 · p. 16
  • At Port Isabel, both approaches progressively lose event amplitude and variability as lead time increases.The example illustrates that reduced recursive degradation need not preserve event-level fidelity.Source: Figure D1 · p. 16, Appendix D · p. 16
  • In Oklahoma, deterministic and diffusion forecasts differ more modestly, consistent with smaller quantitative diffusion gains; at Rockport, diffusion remains bounded while event-level fidelity declines.Together, the examples show numerical stabilization alongside progressive fidelity loss in water-level forecasts.Source: Appendix D · pp. 15, 17, Figure D2 · p. 17

Open Research Section

The study identifies public sources for its water-level and precipitation data and makes the model configurations, rollout procedures, and evaluation code publicly available.

Open Research Section

Related papers

Loading 2609.33930v1…