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Predicting partially observable dynamical systems via diffusion models with a multiscale inference scheme
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Proposes a multiscale inference scheme with exponentially spaced "multiscale templates" for conditional video diffusion models, applied to probabilistic prediction of partially observable solar dynamics using a new 8.5TB multimodal solar active-region dataset.
Problem
Probabilistic prediction of partially observable, long-memory dynamical systems (e.g., solar active regions) where autoregressive rollouts fail to integrate distant past information and accumulate distribution errors.
Approach
Generate video segments with exponentially spaced temporal templates so that each diffusion call conditions on fine-grained present frames and coarse distant past/future frames, enabling a distant future step to be predicted in one call with a fixed-size model.
Key results
- On solar prediction, the multiscale scheme with DiT reaches Wasserstein 3.0 / 4.3 / 5.5 across 1:4, 4:16, 16:32 h windows versus 3.9 / 5.6 / 7.9 for autoregressive rollout.
- On the synthetic sinusoid-plus-noise example, multiscale inference achieves Wasserstein distance 0.021 versus 0.23 for autoregressive.
- Compared with AViT and AR-diffusion baselines, the proposed DiT with multiscale scheme attains lower Wasserstein distance at all horizons (e.g., 5.5 vs 15 and 16 at 16:32 h).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace autoregressive inference with multiscale inference | DiT on solar dynamics · Solar dynamics 1:4 | Wasserstein distance: 3.9 -> 3.0 | Helped |
| Replace autoregressive inference with multiscale inference | DiT on solar dynamics · Solar dynamics 4:16 | Wasserstein distance: 5.6 -> 4.3 | Helped |
| Replace autoregressive inference with multiscale inference | DiT on solar dynamics · Solar dynamics 16:32 | Wasserstein distance: 7.9 -> 5.5 | Helped |
| Replace Hierarchy-2 inference with multiscale inference | DiT on solar dynamics · Solar dynamics 1:4 | Wasserstein distance: 3.0 -> 3.0 | No clear effect |
| Replace Hierarchy-2 inference with multiscale inference | DiT on solar dynamics · Solar dynamics 4:16 | Wasserstein distance: 4.6 -> 4.3 | Helped |
| Replace Hierarchy-2 inference with multiscale inference | DiT on solar dynamics · Solar dynamics 16:32 | Wasserstein distance: 6.0 -> 5.5 | Helped |
| Replace autoregressive inference with multiscale inference | DiT on solar dynamics · Solar dynamics 1:4 | MAE Power Spec.: 0.25 -> 0.12 | Helped |
| Replace autoregressive inference with multiscale inference | DiT on solar dynamics · Solar dynamics 4:16 | MAE Power Spec.: 0.36 -> 0.22 | Helped |
| Replace autoregressive inference with multiscale inference | DiT on solar dynamics · Solar dynamics 16:32 | MAE Power Spec.: 0.53 -> 0.33 | Helped |
| Restrict the multiscale scheme to the same 3-step past horizon as autoregressive inference (ablation) | Multiscale inference on the synthetic sinusoidal series · Synthetic sinusoidal series | Wasserstein distance: 0.021 -> 0.08 | Hurt |
| Replace autoregressive inference with multiscale inference | Diffusion model on the synthetic sinusoidal series · Synthetic sinusoidal series | Wasserstein distance: 0.23 -> 0.021 | Helped |
| Replace autoregressive inference with multiscale inference | Model on partially observable Navier-Stokes · Partially observable Navier-Stokes 4:16 | MAE Power Spectrum: 0.43 -> 0.36 | Helped |
Surprising findings
- Hierarchy-2 scheme gives the lowest error on some metrics (e.g., MAE power spectrum at 1:4 h and NMAE MeanGBT at 1:4 h), outperforming the multiscale scheme there.
- The deterministic AViT achieves the lowest power-spectrum MAE at 1:4 h (0.11) among the compared models, despite worse distributional metrics.
Limitations
- May not remain competitive when observations are dominated by short-term patterns rather than long-memory smooth decay.
- Errors can still grow beyond the largest template's time scale (horizon 9 steps).
Experimental setup
Datasets: SDO HMI magnetograms SDO AIA images PDEArena Navier-Stokes
Benchmarks: Solar active-region test set (2013 and 2019 intervals) PDEArena Navier-Stokes (partially observable density field)
Metrics: Wasserstein distance MAE power spectrum NMAE MeanGBT NMAE MeanGBZ Wasserstein distance on synthetic example
Baselines: Autoregressive rollout Hierarchy-2 (FDM) AViT AR-diffusion
Builds on: Flexible Diffusion Models (FDM) EDM Rolling Diffusion DiT RoPE
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