From Noise to Laws: Regularized Time-Series Forecasting via Denoised Dynamic Graphs
Hongwei Ma, Junbin Gao, Minh-ngoc Tran
TL;DR
PRISM is a novel method for long-horizon multivariate time-series forecasting that denoises signals, models dynamic dependencies, and ensures stability using a diffusion-based approach combined with physics-informed regularization.
Contribution
It introduces PRISM, integrating score-based diffusion, dynamic graph encoding, and physics penalties, with theoretical guarantees and state-of-the-art results on benchmarks.
Findings
Achieves consistent state-of-the-art performance on six benchmarks.
Demonstrates robustness through Lipschitz bounds and contraction properties.
Outperforms existing methods in MSE and MAE metrics.
Abstract
Long-horizon multivariate time-series forecasting is challenging because realistic predictions must (i) denoise heterogeneous signals, (ii) track time-varying cross-series dependencies, and (iii) remain stable and physically plausible over long rollout horizons. We present PRISM, which couples a score-based diffusion preconditioner with a dynamic, correlation-thresholded graph encoder and a forecast head regularized by generic physics penalties. We prove contraction of the induced horizon dynamics under mild conditions and derive Lipschitz bounds for graph blocks, explaining the model's robustness. On six standard benchmarks , PRISM achieves consistent SOTA with strong MSE and MAE gains.
Peer Reviews
Decision·ICLR 2026 Conference Withdrawn Submission
I appreciate the incorporation of the reaction–diffusion prior on the forecast trajectory and the accompanying theoretical development that establishes its stability guarantees. In this regard, one of the strengths of the paper lies in Propositions 1 and 2, which are commendable for the authors’ effort to provide theoretical grounding. These propositions rely on standard arguments that have been previously established in the graph-stability literature, such as [1]. [1] Gama, F., Ribeiro, A. and
I consider the incorporation of the reaction–diffusion prior to be the only element of genuine novelty in this paper. The remaining components appear to be a compilation of previously developed ideas, assembled in a way that does not provide new conceptual insight or a clear methodological rationale for their integration. The paper lacks an overarching research hypothesis or unifying theoretical perspective; rather, it combines several existing modules with limited justification for their joint
The combination of diffusion-based denoising with dynamic graph encoding and regularization appears to be novel in application to LTSF, even though individual components are established. The frequency domain analysis showing preserved fundamentals with attenuated high-frequency noise provides useful diagnostic insight. The authors present ablation studies to disentangle contributions of different components.
I find the "physics-informed" terminology somewhat misleading. The regularizers here are smoothness constraints: velocity/acceleration caps from empirical training percentiles, range clipping from min/max, and a reaction-diffusion residual that is simply graph Laplacian smoothing with learnable parameters. These are heuristic regularizers, not domain physics and invites confusion with genuine physics-based modeling applications where known governing equations are leveraged for data-driven learni
Following are the strengths I can identify : Coherent, practical recipe. Combining input denoising, dynamic graph structure, and lightweight physical constraints is a reasonable direction for stabilizing long-horizon predictions. Some theoretical intuitions are outlined (contraction/conditioning arguments) that aim to justify stability. Ablation sketch suggests each component helps.
**Questionable novelty** : Each module (diffusion denoising, correlation-based dynamic graphs, physics-style penalties) is known; the paper doesn’t clearly isolate what is new beyond the combination, nor why the combination is more than “module stitching.” Although the authors do make a note at the end of the related work section but never explain how everything blends in together. **Hand-wavy Method section** : The method section seemed hand wavy in terms of defining notations properly. Mult
The authors have followed a good system of presenting results, trying to explain them, and then perform ablation studies to establish that each block in the architecture is useful.
1. The writing is dense, and the paper overall is difficult to follow 2. There is heavy use of technical jargon, from the abstracts to the very end, the conclusion. 3. Numerical results are presented without confidence intervals 4. The resolution of Fig 1 is low, and the latex equations are not rendered correctly 5. Some equations are numbered, while others are not.
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Taxonomy
TopicsMachine Learning in Healthcare · Traffic Prediction and Management Techniques · Generative Adversarial Networks and Image Synthesis