How Nvidia’s ERDM Model Beats EDM in Long‑Term Weather Forecasting (NeurIPS 2025)

Researchers from Nvidia and UC San Diego extend the Elucidated Diffusion Model (EDM) framework to address the challenges of probabilistic forecasting for chaotic dynamical systems. By systematically improving noise scheduling, denoiser network parametrization, preprocessing, loss‑weighting, and sampling, they construct the Enhanced Rolling Diffusion Model (ERDM).

Background and Motivation

Mid‑term weather forecasting (≤15 days) remains difficult because atmospheric dynamics are highly sensitive to initial conditions, causing small errors to amplify rapidly. Traditional ensemble numerical weather prediction scales exponentially in computational cost as accuracy and lead time increase, prompting a shift toward data‑driven approaches.

Rolling Sequence Diffusion Models (RSDM) adopt progressive noise schedules to mimic increasing uncertainty over time, but they inherit architectural limitations from early DDPM designs. EDM, awarded Best Paper at NeurIPS 2022, unifies and improves DDPM, offering better training stability and generation quality. Integrating EDM’s time‑loss weighting into RSDM promises higher modeling precision and efficiency.

ERDM Design

ERDM combines the RSDM idea of “noise that grows with prediction horizon” with EDM’s normalized design. Key innovations include:

Progressive noise schedule: The generation window is split into consecutive segments, each assigned a distinct noise level that smoothly transitions between segments. During training the model samples random noise levels; during inference noise decays from a high initial level to a clean output.

Probabilistic ODE control: An ordinary differential equation governs the addition and removal of noise, providing a deterministic “navigation map” for the diffusion trajectory. At each inference step the ODE is solved numerically, producing a partially denoised state that seeds the next rolling window.

Denoiser network: Built on EDM’s standardized preprocessing, the network learns to recover clean sequences from noisy inputs. Training uses an uncertainty‑aware weighting scheme that gives higher weight to intermediate‑noise samples, encouraging the model to master crucial mid‑trajectory states.

Architecture: ERDM replaces 2‑D and costly 3‑D convolutions with a hybrid 2‑D U‑Net plus temporal‑attention module. The U‑Net extracts spatial features per timestep, while temporal attention captures inter‑timestep dependencies. Noise embeddings are injected via regularization layers.

Datasets

Navier‑Stokes: A 221×42 grid with random circular obstacles, fluid viscosity fixed at 1×10⁻³. Each case records x‑velocity, y‑velocity, and pressure fields; boundary conditions and obstacle masks are provided as auxiliary inputs. The task is to predict 64 future timesteps from a single initial state.

ERA5 Reanalysis: 1.5° resolution (240×212 grid) covering 69 variables (13 pressure levels of temperature, geopotential height, specific humidity, wind components; plus surface temperature, mean sea‑level pressure, 10‑m wind). Training uses hourly data from 1979‑2020; evaluation selects 64 distinct initial conditions from 2021 (00 UTC and 12 UTC) to assess mid‑term forecast performance.

Experimental Evaluation

Two core metrics are used:

Continuous Ranked Probability Score (CRPS) – lower values indicate better overall forecast accuracy.

Spread‑Skill Ratio (SSR) – compares ensemble variance to mean error; values near 1 denote well‑calibrated uncertainty.

On the Navier‑Stokes benchmark, ERDM outperforms the best EDM baseline by roughly 50 % in CRPS for later timesteps, while EDM shows a slight edge at early steps. ERDM also maintains superior uncertainty calibration, avoiding the under‑dispersion observed in EDM.

For the ERA5 mid‑term weather task, ERDM is trained on four H100 GPUs for five days—significantly less than other data‑driven methods. It consistently beats the internal EDM baseline, achieving up to a 10 % CRPS improvement and surpassing Graph‑EFM. Compared with operational IFS ENS and NeuralGCM ENS, ERDM is competitive but lags slightly on short‑term variables, a gap attributed to the initial‑field construction strategy.

In terms of physical realism, ERDM’s 14‑day forecast power spectra align closely with IFS ENS, whereas NeuralGCM underestimates energy in mid‑high frequency bands.

Broader Impact

The study situates ERDM within a growing ecosystem of physics‑aware AI for fluid dynamics and weather prediction. Parallel academic efforts (e.g., DeepMind + NYU’s PINN‑Gaussian‑Newton work) and industry deployments (Huawei’s Tianzi‑12h, Amazon’s DeepAR) illustrate the expanding relevance of probabilistic sequence models across scientific and engineering domains.

Future directions include tighter integration with deterministic solvers, improved initialization strategies for ensemble forecasts, and extending the ERDM framework to robotics, energy scheduling, and biological dynamics.