Title: Collaborative Deterministic–Probabilistic Forecasting for Real-World Spatiotemporal Systems
Venue: NeurIPS 2025
Accepted: no
Keywords: Spatiotemporal forecasting

probabilistic forecasting

diffusion models
Abstract: Probabilistic forecasting is crucial for real-world spatiotemporal systems, such as climate, energy, and urban environments, where quantifying uncertainty is essential for informed, risk-aware decision-making. While diffusion models have shown promise in capturing complex data distributions, their application to spatiotemporal forecasting remains limited due to complex spatiotemporal dynamics and high computational demands. In this work, we propose CoST, a novel framework that collaborates deterministic and diffusion models for spatiotemporal forecasting. 
CoST formulates a mean-residual decomposition strategy: it leverages a powerful deterministic model to capture the conditional mean and a lightweight diffusion model to learn residual uncertainties
This collaborative formulation simplifies learning objectives, enhances forecasting accuracy, enables uncertainty quantification, and significantly improves computational efficiency. To address spatial heterogeneity, we further design a scale-aware diffusion mechanism to guide the diffusion process. Extensive experiments across ten real-world datasets from climate, energy, communication, and urban systems show that CoST achieves 25% performance gains over state-of-the-art baselines, while significantly reducing computational cost. Code and datasets are available at: https://anonymous.4open.science/r/CoST_8069.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces CoST, a collaborative deterministic–probabilistic forecasting framework designed for real-world spatiotemporal systems. Recognizing the complexity of fully probabilistic modeling using diffusion models alone, CoST employs a mean-residual decomposition approach, where a deterministic model predicts the conditional mean, and a diffusion model focuses on residual uncertainties. A scale-aware diffusion mechanism addresses spatial heterogeneity, enhancing the model's flexibility and accuracy. Experimental evaluations across various domains—including climate, energy, communication, and urban systems—demonstrate that CoST significantly outperforms existing state-of-the-art methods, achieving an average improvement of 25% on key metrics, while notably reducing computational costs.\n\nSTRENGTHS AND WEAKNESSES:\nThe innovations highlighted by the authors appear to overlap significantly with previously published works, such as TMDM. The authors should explicitly clarify how CoST differs from TMDM.\n\nThe model configuration proposed by the authors closely resembles that of TMDM; the distinctions need to be clearly articulated.\n\nNumerous existing studies have already investigated signal decomposition into two or more components for forecasting. The authors must specify how CoST differentiates itself from these studies [2,3].\n\nThe experiments need to include comprehensive comparisons with various existing methods, as the current evaluation is insufficient.\n\n[1] Li, Y., Chen, W., Hu, X., Chen, B., & Zhou, M. (2024). Transformer-modulated diffusion models for probabilistic multivariate time series forecasting. In The Twelfth International Conference on Learning Representations.\n\n[2] Wang, S., Wu, H., Shi, X., Hu, T., Luo, H., Ma, L., ... & Zhou, J. (2024). Timemixer: Decomposable multiscale mixing for time series forecasting. arXiv preprint arXiv:2405.14616.\n\n[3] Yu, G., Zou, J., Hu, X., Aviles-Rivero, A. I., Qin, J., & Wang, S. (2024). Revitalizing multivariate time series forecasting: Learnable decomposition with inter-series dependencies and intra-series variations modeling. arXiv preprint arXiv:2402.12694.\n\nQUESTIONS:\nSee summary or Weaknesses.\n\nLIMITATIONS:\nSee summary or Weaknesses.", "TITLE": "Official Review", "RECOMMENDATION": 2, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 1, "ORIGINALITY": 1, "DATE": "2025-06-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents CoST, a novel collaborative framework for spatiotemporal forecasting that unifies deterministic and probabilistic modeling in a synergistic way. CoST decomposes the spatiotemporal forecasting task into a deterministic prediction (capturing the main trend) and a probabilistic residual prediction (modeling uncertainty and stochastic variation). Extensive experiments across six spatiotemporal benchmarks demonstrate that CoST significantly outperforms SOTA baselines in terms of accuracy, uncertainty quantification, and robustness.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n\nS1.\tThis paper has a clear motivation and well-defined problem setting. It addresses a fundamental trade-off in spatiotemporal forecasting: accuracy vs. uncertainty, and proposes a hybrid framework that leverages the strengths of both deterministic and probabilistic modeling. The ability to provide accurate predictions along with calibrated uncertainty estimates is essential for real-world applications in spatiotemporal systems.\n\nS2.\tTheoretical analysis of the mean-residual decomposition offers support for the collaborative design of CoST. This theoretical grounding enhances the credibility of the proposed architecture.\n\nS3.\tThe empirical evaluation is extensive and convincing. Experiments span diverse domains, including urban systems, communication networks, climate systems, and renewable energy, and demonstrate consistent improvements over both classical and SOTA baselines.\n\nS4.\tThe paper is well-written and logically structured.\n\n\n**Weakness:**\n\nThe joint training of the deterministic model and the diffusion model introduces added complexity and may increase optimization time.\n\nQUESTIONS:\nQ1.\tI am particularly interested in how CoST performs under extreme cases. Could the authors elaborate on the mechanisms that allow it to handle such cases effectively?\n\nQ2.\tDoes the probabilistic component always refine the deterministic output? Are there failure cases where they conflict?\n\nQ3.\tHow can the learned uncertainty estimates be effectively used in downstream decision-making tasks, such as traffic management, public safety alerts, or ride-sharing dispatch?\n\nLIMITATIONS:\nThe authors have discussed the limitations of this approach. Besides, inference cost of diffusion models may pose challenges in real-time applications without acceleration strategies.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-25"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces CoST, a spatiotemporal forecasting method that hybridizes deterministic forecasting model and diffusion model. CoST uses a deterministic model to capture the conditional mean of the spatiotemporal data, and applies the diffusion model to learn the residuals. Since the residual distribution is not i.i.d, the author proposed the \"scale-aware diffusion process\", which employs FFT to extract the fluctuation components for each spatial unit. The variance of the residual fluctuations are used to formulate the prior in diffusion model. The framework works for both regular grid data and data on graphs due to the adoption of FFT. The author conducted experiments on five real-world spatiotemporal forecasting datasets and reported performance boost over pure diffusion models via CoST.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. CoST frameworks works for both grid-structured spatiotemporal data and graph-structured spatiotemporal data and boosts the performance over pure diffusion model consistently, as shown in Table 3.\n2. The author demonstrated that the \"scale-aware diffusion process\" boosts the model performance in Figure 8 in Appendix.\n3. The author adopts probabilistic evaluation metrics like QICE and IS to evaluate the model performance. The analysis in Section 5.3 is intuitive and demonstrates the CoST captures the probabilistic distribution better.\n\nWeakness:\n1. The idea of hybridizing deterministic forecasting model and diffusion model has been explored in DiffCast (https://openaccess.thecvf.com/content/CVPR2024/papers/Yu_DiffCast_A_Unified_Framework_via_Residual_Diffusion_for_Precipitation_Nowcasting_CVPR_2024_paper.pdf) and CasCast (https://arxiv.org/pdf/2402.04290). Hybridizing these two types of forecasting model is not a novel idea.\n2. Following the first weakness, the author also did not compare with other methods for handling non-i.i.d residual errors. For example, DiffCast build an auto-regressive model that predicts the residual map at timestamp t with the predicted residual map at timestamp t-1.\n\nAlso, minor typo in line 199. reprent --> represent.\n\nQUESTIONS:\nI may have misunderstood the results but how did you remove the scale-aware diffusion process (w/o s) while keeping the customized fluctuation scale as a prior (w/o q)? I need more clarification about the experiment setting used in Figure 8. According to Section 4.3, the customized fluctuation scale is part of the scale-aware diffuion process. I'm not sure how to apply scale-aware diffusion process without the customized fluctuation scale, or how to apply customized fluctuation scale without the scale-aware diffusion process.\n\nLIMITATIONS:\nYes, the limitations are mentioned in Section 6.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a simple approach for multivariate probabilistic forecasting by decoupling the learning process into two distinct components. First, a deterministic model is trained to predict the mean of the forecast distribution. Subsequently, a diffusion model is conditioned on this predicted mean to capture the complex, time-varying uncertainties and dependencies inherent in the multivariate data. The experimental results demonstrate that this decomposition strategy leads to improved performance on univariate evaluation metrics.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n\n(S1) The proposed method is straightforward and well-explained, making it easy for other researchers to understand and replicate the experiments.\n\n(S2) The paper is clearly written and logically structured, which effectively communicates the authors' ideas and findings.\n\nWeaknesses\n\n(W1) The primary goal of the paper is multivariate probabilistic forecasting, yet the evaluation relies solely on univariate scoring rules. This is a significant limitation, as it fails to assess the model's ability to capture the joint distribution and dependencies between the different time series. The inclusion of multivariate scoring rules, such as the Energy Score or Variogram Score, is essential for a complete and accurate evaluation.\n\n(W2) The paper focuses heavily on diffusion models but overlooks a number of widely used and relevant baseline models for probabilistic multivariate forecasting. A more thorough comparison against established methods like DeepAR, DeepStateSpace, or models based on Normalizing Flows would provide a more convincing case for the proposed model's effectiveness and better contextualize its contributions.\n\n(W3) The core weakness lies in the justification for using a diffusion model. While diffusion models excel at capturing highly complex, multimodal distributions, the paper does not provide strong evidence that short-term time series forecasting benefits from such a powerful and computationally intensive model. The motivation would be stronger if the authors could demonstrate, for instance, that the forecasting task involves complexities that simpler models like Gaussian processes or traditional state-space models cannot handle.\n\nQUESTIONS:\n(Q1) The results suggest that conditioning on a predicted mean is beneficial. Could a simpler, non-parametric mean achieve similar results? For instance, have you considered using a simple historical average (e.g., the value from the previous season) or a global mean as the conditional input for the diffusion model? An ablation study with these simpler mean functions would help clarify whether the performance gain comes from the sophisticated deterministic model or simply from providing mean guidance.\n\n(Q2) Could you please elaborate on how the \"ideal\" multimodal distribution in Figure 4 was derived? In a real-world forecasting task, the ground truth is a single future value, not a distribution. Understanding how this target distribution was generated is crucial for interpreting the model's qualitative performance.\n\n(Q3) Could you specify how the CRPS was calculated? Sample-based or closed-form? For other metrics, are 50 samples sufficient in obtaining a reliable metric?\n\nLIMITATIONS:\nyes.", "TITLE": "Official Review", "RECOMMENDATION": 2, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 1, "ORIGINALITY": 1, "DATE": "2025-07-02"}