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CogDPM: Diffusion Probabilistic Models via Cognitive Predictive Coding
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Proposes CogDPM, a diffusion probabilistic model that embeds predictive coding (hierarchical inference, prediction-error guidance, precision weighting via denoising-trajectory variance) for spatiotemporal forecasting on MovingMNIST, turbulence, ERA5 wind, and UK precipitation.
Problem
Existing PC-inspired spatiotemporal prediction networks (e.g., PredNet) do not improve real-world forecasting and ignore precision weighting; diffusion models lack a predictive-coding-based formulation for scientific field forecasting.
Approach
Couple a generative DPM (unconditional) with a perceptual DPM (conditional) sharing parameters, use their difference as prediction-error guidance, and weight it by an inverse-precision field estimated as the variance of direct x0 predictions along the denoising trajectory.
Key results
- On MovingMNIST, CogDPM reports CRPS 0.0697 and CSI 0.7365 versus 0.0820 and 0.6959 for the naive classifier-free-guidance DPM.
- On the UK precipitation nowcasting task, CogDPM outperforms the operational DGMR model in CRPS, economic value and PSD (qualitative and aggregated scores reported in figures).
- On ERA5 wind forecasting, CogDPM shows lower CRPS across all prediction times and better CSI than FourCastNet, especially at heavier wind thresholds.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add precision-weighted guidance to vanilla DPM (ablation) | DPM · MovingMNIST | CRPS (avg): 0.0323 -> 0.027 | No clear effect |
| Add precision-weighted guidance to vanilla DPM (ablation) | DPM · MovingMNIST | CRPS (max): 0.082 -> 0.0697 | Helped |
| Add precision-weighted guidance to vanilla DPM (ablation) | DPM · MovingMNIST | CSI: 0.6959 -> 0.7365 | Helped |
| Add precision-weighted guidance to vanilla DPM (ablation) | DPM · MovingMNIST | FSS: 0.822 -> 0.8588 | Helped |
| Add precision-weighted guidance to vanilla DPM (ablation) | DPM · Turbulence | CRPS (avg): 0.0023 -> 0.0023 | No clear effect |
| Add precision-weighted guidance to vanilla DPM (ablation) | DPM · Turbulence | CRPS (max): 0.0096 -> 0.0034 | Helped |
| Add precision-weighted guidance to vanilla DPM (ablation) | DPM · Turbulence | CSI: 0.6725 -> 0.7962 | Helped |
| Add precision-weighted guidance to vanilla DPM (ablation) | DPM · Turbulence | FSS: 0.9668 -> 0.9722 | Helped |
| Replace constant classifier-free guidance with precision-weighted guidance (ablation) | VDM · ERA5 surface wind | CSI | Mixed |
| Replace constant classifier-free guidance with precision-weighted guidance (ablation) | VDM · ERA5 surface wind | CRPS | Helped |
Surprising findings
- Monte Carlo sampling-based precision estimates were reported to fail in the fluid case due to over-confidence, while the trajectory-variance precision remained informative.
Limitations
- Active inference is omitted from the framework and left to future work.
- Precision weights are an approximation of true precision since only past observations are available at forecast time.
Experimental setup
Datasets: MovingMNIST Turbulence flow ERA5 reanalysis UK precipitation (Met Office RadarNet4)
Benchmarks: MovingMNIST Turbulence flow ERA5 surface wind UK precipitation nowcasting
Metrics: CRPS CSI FSS RMSE neighborhood CRPS economic value power spectral density
Baselines: FourCastNet DGMR MotionRNN PhyDNet PredRNN-v2 DPM with classifier-free guidance VDM
Builds on: PredNet classifier-free diffusion guidance DDPM video diffusion models
Closest papers by meaning
- Dynamical Diffusion: Learning Temporal Dynamics with Diffusion Models (ICLR 2025 · similarity 0.86)
- CogReact: A Reinforced Framework to Model Human Cognitive Reaction Modulated by Dynamic Intervention (ICML 2025 · similarity 0.85)
- Divide-and-Conquer Predictive Coding: a structured Bayesian inference algorithm (NeurIPS 2024 · similarity 0.85)
- Understanding Sample Efficiency in Predictive Coding (NeurIPS 2026 · similarity 0.85)
- Interacting Diffusion Processes for Event Sequence Forecasting (ICML 2024 · similarity 0.84)
- Why Diffusion Models Don’t Memorize: The Role of Implicit Dynamical Regularization in Training (NeurIPS 2025 · similarity 0.84)
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