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From Noise to Laws: Regularized Time-Series Forecasting via Denoised Dynamic Graphs

Hongwei Ma, Junbin Gao, Minh-ngoc Tran

TL;DR

PRISM addresses the challenge of long-horizon multivariate time-series forecasting by integrating diffusion-based denoising, dynamic correlation graphs, and physics-inspired regularizers into a unified end-to-end framework. The method provides theoretical guarantees of horizon contraction and Lipschitz stability for graph blocks, and empirically achieves state-of-the-art performance across six diverse benchmarks with improved MSE/MAE and preserved low-frequency structure. Key innovations include a diffusion preconditioner for denoising, a thresholded dynamic graph encoder for regime-adaptive message passing, and reaction–diffusion–based stabilization with kinematic and lag-coherence penalties. The results demonstrate enhanced robustness to noise, nonstationarity, and long-horizon drift, with practical implications for engineering systems requiring reliable, interpretable forecasts.

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.

From Noise to Laws: Regularized Time-Series Forecasting via Denoised Dynamic Graphs

TL;DR

PRISM addresses the challenge of long-horizon multivariate time-series forecasting by integrating diffusion-based denoising, dynamic correlation graphs, and physics-inspired regularizers into a unified end-to-end framework. The method provides theoretical guarantees of horizon contraction and Lipschitz stability for graph blocks, and empirically achieves state-of-the-art performance across six diverse benchmarks with improved MSE/MAE and preserved low-frequency structure. Key innovations include a diffusion preconditioner for denoising, a thresholded dynamic graph encoder for regime-adaptive message passing, and reaction–diffusion–based stabilization with kinematic and lag-coherence penalties. The results demonstrate enhanced robustness to noise, nonstationarity, and long-horizon drift, with practical implications for engineering systems requiring reliable, interpretable forecasts.

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.
Paper Structure (61 sections, 4 theorems, 27 equations, 5 figures, 4 tables, 3 algorithms)

This paper contains 61 sections, 4 theorems, 27 equations, 5 figures, 4 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Background and challenge.
  3. Gaps in existing paradigms.
  4. Design hypothesis: a causal chain.
  5. The PRISM framework.
  6. Contributions.
  7. Positioning.
  8. Related Works
  9. Methodology
  10. Problem Setup and Notation
  11. Series-wise Denoising via Diffusion Model
  12. Dynamic Graph Construction from Correlations
  13. Temporal Encoder
  14. Configurable Graph Encoder
  15. Configurable Decoder
  16. ...and 46 more sections

Key Result

Proposition 1

Let $\bar{A}_t=\bar{A}_t^\top\succeq 0$ with $\rho(\bar{A}_t)\le 1$, and define the linearized horizon map $M(\kappa,\gamma;\bar{A}_t)=(1-\gamma-\kappa)I+\kappa\,\bar{A}_t.$ If $0<\kappa<1$, $0<\gamma<1$, and $\kappa+\gamma<1$, then $\rho(M(\kappa,\gamma;\bar{A}_t))<1$. Consequently, the recurrence

Figures (5)

  • Figure 1: The overall architecture of DORIC
  • Figure 2: Frequency-Domain Analysis
  • Figure D.1: Ablation deltas computed from the body tables (exact values reproduced).
  • Figure D.2: Average relative degradation across datasets (%); derived from body ablations.
  • Figure E.3: Thresholded correlation adjacencies used by PRISM. Bright cells survive $|C_t|>\tau$ and are reweighted by $|C_t|^{\gamma}$; black cells are pruned. Self-loops are added only after normalization when forming $\bar{A}_t$.

Theorems & Definitions (8)

  • Proposition 1: Stability of the reaction--diffusion step
  • Proposition 2: Lipschitz bound for a graph block
  • proof
  • Lemma 1: Uniform contraction over $t$
  • proof
  • Lemma 2: Perturbation margin
  • proof
  • proof