GARDiff: Graph-Aligned Residual Diffusion for Probabilistic Multivariate Time-Series Forecasting

Rui Han; Min Yang; Xu Zhang; Xinghao Yang; Wei Liu; Yongshun Gong

cs.LGSep 29, 2026

GARDiff: Graph-Aligned Residual Diffusion for Probabilistic Multivariate Time-Series Forecasting

Authors: Rui Han, Min Yang, Xu Zhang, Xinghao Yang, Wei Liu, Yongshun Gong

Organizations: Shandong University, Jinan, China · Macquarie University, Sydney, Australia · China University of Petroleum (East China), Qingdao, China · University of Technology Sydney, Sydney, Australia

Abstract

Diffusion models have recently shown strong potential for probabilistic multivariate time-series forecasting by modeling complex conditional distributions. Recent decoupled diffusion frameworks further separate forecasting into deterministic prediction and stochastic residual generation, making it natural to derive dependency graphs from deterministic representations and use them to guide residual diffusion. However, we show that this direct structural transfer is unreliable. Although deterministic-derived graphs encode useful global dependency priors, they exhibit substantial edge-level misalignment with residual dependency structures, introducing inaccurate or redundant conditions during residual generation. This reveals a previously overlooked deterministic-to-residual structural alignment problem in decoupled diffusion forecasting. To address this problem, we propose GARDiff, a Graph-Aligned Residual Diffusion framework for probabilistic multivariate time-series forecasting. Instead of treating deterministic-derived graphs as fixed diffusion conditions, GARDiff progressively adapts them to residual generation. Specifically, GARDiff estimates residual uncertainty to distinguish high- and low-uncertainty regions, enabling uncertainty-aware structural refinement, and further performs timestep-aware edge sparsification during reverse diffusion to evolve graph conditions from broad dependency aggregation to localized residual refinement. Extensive experiments on six real-world benchmarks demonstrate that GARDiff consistently improves probabilistic forecasting performance and uncertainty calibration over strong baselines.

Figures & tables

Figure 1: (a) Comparison between existing diffusion forecasting and the decoupled forecasting paradigm. Decoupling deterministic and uncertainty modeling enables the deterministic stage to provide structural priors for uncertainty-aware residual diffusion. (b) Quantitative evidence of structural mismatch between deterministic-derived and residual-derived graphs.

Figure 2: Overview of GARDiff. The deterministic forecasting module extracts representations and constructs a structural prior graph. The graph alignment module refines the prior using residual uncertainty and diffusion timestep. The graph-conditioned diffusion module then performs residual generation with dynamic structural guidance.

Model	ETTm1		ETTm2		Weather		Solar		ECL		Traffic
Model	CRPS	$\mathrm{CRPS}_{\mathrm{sum}}$	CRPS	$\mathrm{CRPS}_{\mathrm{sum}}$	CRPS	$\mathrm{CRPS}_{\mathrm{sum}}$	CRPS	$\mathrm{CRPS}_{\mathrm{sum}}$	CRPS	$\mathrm{CRPS}_{\mathrm{sum}}$	CRPS	$\mathrm{CRPS}_{\mathrm{sum}}$
TimeDiff	0.490	2.195	0.320	1.597	0.302	2.625	0.700	2.408	0.735	1.966	0.766	1.885
TMDM	0.380	1.665	0.298	1.412	0.244	1.915	0.355	1.534	0.438	1.573	0.453	1.587
NsDiff	0.394	1.878	0.315	1.564	0.230	1.971	0.273	0.951	0.285	0.874	0.319	0.864
D3U	0.283	0.801	0.247	0.114	0.208	0.248	0.174	0.604	0.202	0.665	0.224	0.786
Ours	0.273	0.744	0.234	0.093	0.199	0.220	0.166	0.463	0.191	0.459	0.212	0.459

Table 1: Probabilistic forecasting performance. All results are reported with input length

H{=}96

and averaged over three forecasting horizons (

L\in\{96,192,336\}

). Best results are highlighted in bold . See Table 6 for full results.

Point Forecasting Models
Model	ETTm1		ETTm2		Weather		Solar		ECL		Traffic
Model	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
PatchTST	0.359	0.381	0.247	0.304	0.227	0.258	0.242	0.275	0.177	0.263	0.455	0.287
TimesNet	0.386	0.404	0.254	0.307	0.225	0.263	0.251	0.272	0.186	0.288	0.613	0.325
iTransformer	0.381	0.397	0.252	0.312	0.227	0.257	0.231	0.257	0.164	0.256	0.411	0.276
TimeBridge	0.360	0.375	0.244	0.307	0.221	0.248	0.220	0.230	0.155	0.256	0.411	0.273

Table 2: Deterministic forecasting performance. All results are reported with input length

H{=}96

and averaged over three forecasting horizons (

L\in\{96,192,336\}

). Best results are highlighted in bold . See Table 7 for full results.

Dataset	Setting	MSE	MAE	CRPS	$\mathbf{CRPS}_{\mathbf{sum}}$
ETTm1	Pred. Unc.	0.345	0.375	0.273	0.744
ETTm1	Oracle Res.	0.346	0.375	0.272	0.751
Weather	Pred. Unc.	0.222	0.268	0.202	0.220
Weather	Oracle Res.	0.222	0.268	0.202	0.220

Table 3: Performance comparison between predicted uncertainty and oracle residuals. Results are reported with input length

H{=}96

and averaged over three forecasting horizons (

L\in\{96,192,336\}

). See Table 9 for full results.

Explore similar work

DynG-Diff: A State-Aware Dynamic Guidance Diffusion Framework for Probabilistic Time Series Forecasting
Sep 2, 2026Zhente Zhang, Zhengwei Ni, Wei FanMultivariate Time Series Forecasting Probabilistic Forecasting
School of Information and Electronic Engineering (Sussex Artificial Intelligence Institute), Zhejiang Gongshang University, Hangzhou, Zhejiang, China · School of Computer Science, University of Auckland, Auckland, New Zealand
RDDMPI: Residual Denoising Diffusion Model for Probabilistic Multivariate Time Series Imputation
Sep 10, 2026Ramiro Valdes Jara, David Chapman, Adam MeyersImputation Residual Conditional Diffusion Model
Department of Industrial and Systems Engineering, University of Miami, United States of America · Department of Computer Science, University of Miami, United States of America
Double-Diffusion: Balancing Speed, Accuracy, and Uncertainty in Probabilistic Forecasting for Urban Sensor Networks
Jun 29, 2025Hanlin Dong, Arian Prabowo, Hao Xue +4Probabilistic Forecasting Diffusion Dynamics
University of New South Wales Sydney, Australia · University of Maryland College Park, United States · The Hong Kong University of Science and Technology (Guangzhou) Guangzhou, China

Sep 2, 2026, cs.LGJ/K move · Enter open · S save

DynG-Diff: A State-Aware Dynamic Guidance Diffusion Framework for Probabilistic Time Series Forecasting

Zhente Zhang, Zhengwei Ni, Wei Fan

School of Information and Electronic Engineering (Sussex Artificial Intelligence Institute), Zhejiang Gongshang University, Hangzhou, Zhejiang, China · School of Computer Science, University of Auckland, Auckland, New Zealand

Multivariate Time Series Forecasting Probabilistic Forecasting Diffusion Models

Open paper AskPDF arXiv

Probabilistic multivariate time series (MTS) forecasting is crucial for modeling complex dynamical systems. However, existing diffusion-based methods rely on task-specific conditional paradigms that lack flexibility and struggle with inherent "information heterogeneity"--the significantly varying noise levels and evolutionary patterns across variables. To address this, we propose DynG-Diff, a variable-sensitive dynamic guidance diffusion framework for probabilistic multivariate time-series forecasting: (1) DynG-Diff adopts a two-stage separated training strategy and uses an unconditional diffusion backbone to model the joint distribution of multivariate time series. (2) DynG-Diff introduces a lightweight state-aware policy network that adaptively infers variable reliability from real-time noisy states and one-step denoising estimates, outputting a dynamic guidance strength matrix. (3) DynG-Diff mathematically formulates this dynamic weight as the local precision of the observation distribution, enabling precise guidance for high-confidence variables during inference while filtering out interference from anomalous noise. Extensive experiments on real-world benchmarks demonstrate competitive probabilistic forecasting performance against state-of-the-art conditional diffusion models and improved robustness under severe observation corruption.The implementation code is available at: https://github.com/TT-20011031/DynG-Diff

Abstract

Explore similar work

DynG-Diff: A State-Aware Dynamic Guidance Diffusion Framework for Probabilistic Time Series Forecasting

RDDMPI: Residual Denoising Diffusion Model for Probabilistic Multivariate Time Series Imputation

Double-Diffusion: Balancing Speed, Accuracy, and Uncertainty in Probabilistic Forecasting for Urban Sensor Networks