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CogDPM: Diffusion Probabilistic Models via Cognitive Predictive Coding

Kaiyuan Chen, Xingzhuo Guo, Yu Zhang, Jianmin Wang, Mingsheng Long

TL;DR

CogDPM links Predictive Coding with Diffusion Probabilistic Models to address hierarchical prediction and precision weighting in spatiotemporal forecasting. It introduces a precision-weighted guidance mechanism derived from diffusion denoising steps and a joint perceptual and generative DPM framework. Experiments on synthetic data and real-world weather datasets (UK precipitation, ERA5 wind) show CogDPM achieves superior probabilistic forecasts and provides interpretable precision maps that indicate data predictability. This approach offers improved forecasting reliability and decision-support by delivering both accurate forecasts and calibrated uncertainty.

Abstract

Predictive Coding (PC) is a theoretical framework in cognitive science suggesting that the human brain processes cognition through spatiotemporal prediction of the visual world. Existing studies have developed spatiotemporal prediction neural networks based on the PC theory, emulating its two core mechanisms: Correcting predictions from residuals and hierarchical learning. However, these models do not show the enhancement of prediction skills on real-world forecasting tasks and ignore the Precision Weighting mechanism of PC theory. The precision weighting mechanism posits that the brain allocates more attention to signals with lower precision, contributing to the cognitive ability of human brains. This work introduces the Cognitive Diffusion Probabilistic Models (CogDPM), which demonstrate the connection between diffusion probabilistic models and PC theory. CogDPM features a precision estimation method based on the hierarchical sampling capabilities of diffusion models and weight the guidance with precision weights estimated by the inherent property of diffusion models. We experimentally show that the precision weights effectively estimate the data predictability. We apply CogDPM to real-world prediction tasks using the United Kindom precipitation and ERA surface wind datasets. Our results demonstrate that CogDPM outperforms both existing domain-specific operational models and general deep prediction models by providing more proficient forecasting.

CogDPM: Diffusion Probabilistic Models via Cognitive Predictive Coding

TL;DR

CogDPM links Predictive Coding with Diffusion Probabilistic Models to address hierarchical prediction and precision weighting in spatiotemporal forecasting. It introduces a precision-weighted guidance mechanism derived from diffusion denoising steps and a joint perceptual and generative DPM framework. Experiments on synthetic data and real-world weather datasets (UK precipitation, ERA5 wind) show CogDPM achieves superior probabilistic forecasts and provides interpretable precision maps that indicate data predictability. This approach offers improved forecasting reliability and decision-support by delivering both accurate forecasts and calibrated uncertainty.

Abstract

Predictive Coding (PC) is a theoretical framework in cognitive science suggesting that the human brain processes cognition through spatiotemporal prediction of the visual world. Existing studies have developed spatiotemporal prediction neural networks based on the PC theory, emulating its two core mechanisms: Correcting predictions from residuals and hierarchical learning. However, these models do not show the enhancement of prediction skills on real-world forecasting tasks and ignore the Precision Weighting mechanism of PC theory. The precision weighting mechanism posits that the brain allocates more attention to signals with lower precision, contributing to the cognitive ability of human brains. This work introduces the Cognitive Diffusion Probabilistic Models (CogDPM), which demonstrate the connection between diffusion probabilistic models and PC theory. CogDPM features a precision estimation method based on the hierarchical sampling capabilities of diffusion models and weight the guidance with precision weights estimated by the inherent property of diffusion models. We experimentally show that the precision weights effectively estimate the data predictability. We apply CogDPM to real-world prediction tasks using the United Kindom precipitation and ERA surface wind datasets. Our results demonstrate that CogDPM outperforms both existing domain-specific operational models and general deep prediction models by providing more proficient forecasting.
Paper Structure (27 sections, 15 equations, 8 figures, 2 tables, 1 algorithm)

This paper contains 27 sections, 15 equations, 8 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Predictive Learning.
  4. Predictive Coding.
  5. Predictive Coding Neural Networks.
  6. Method
  7. CogDPM via Predictive Coding
  8. Hierarchical Inference.
  9. Prediction Error Minimization.
  10. Precision Weighting in CogDPM
  11. Experiments
  12. Synthesis Data Experiments
  13. Benchmarks.
  14. Numerical Results
  15. Interpretability of precision weights.
  16. ...and 12 more sections

Figures (8)

  • Figure 1: a, A general predictive coding framework. The system recognizes the sensation fields with hierarchy error units and expectation units and generates the predictions and precision maps during the process. b, Cognitive Diffusion Probabilistic Models (CogDPM) framework, providing predictions and precision weights with multi-step denoising process. c, Updates of latent states with precision-weighted predictive error.
  • Figure 2: Predictions and inverse precision of CogDPM on rigid-body MovingMNIST dataset (left) and Turbulence flow dataset (right).
  • Figure 3: Experiments on high wind forecasting.a, a Case study of the ERA5 wind forecast from 2017-03-04 18:00. High wind and tornadoes attacked the Mideast USA at 2017-03-06 18:00(T=48h) Tornado06March2017. CogDPM provides alarming forecasts, covering states with the most severe weather reports, Iowa and Missouri. CogDPM precision indicate the credibility of the predictions, helping forecasters to identify the missing and false positive regions. b, Numerical scores on ERA5 wind dataset from 2017-01-01 to 2019-12-31. We report CSI with 12 m/s (first) and 16 m/s (second) threshold, RMSE (third), and CRPS across four ensembles (fourth).
  • Figure 4: Experiments on precipitation nowcasting. Case study on an extreme precipitation event starting on 2019-07-24 at 03:15 in the UK timezone, CogDPM successfully predicts movement and intensity variation of the squall front, while DGMR produces results with early dissipation.
  • Figure 5: Experiments on precipitation nowcasting. Numerical verification scores on sampled the United Kingdom precipitation dataset in 2019. CRPS is computed with four ensembles for spatial pooling size 1km x 1km (left top) and 2 km x 2 km (right top); Economic value with 20 mm/h accumulative rain threshold (left bottom); Radially averaged power spectral density on predictions at 90 minutes (right bottom). CogDPM surpasses the operational forecast model DGMR in ensemble forecasting precision and forecast skillfulness.
  • ...and 3 more figures