Graph aligned diffusion improves probabilistic multivariate forecasting
GARDiff: Graph-Aligned Residual Diffusion for Probabilistic Multivariate Time-Series Forecasting
Machine LearningArtificial Intelligence
Summary
Predicting multiple things that change over time is tricky because their values can depend on each other in complex ways. The authors show that using graphs from straightforward predictions to guide the random parts of more advanced models causes problems because the connections in the graph don’t match perfectly. To fix this, they propose a method called GARDiff that adjusts the graph step-by-step based on how uncertain the predictions are, improving forecast accuracy and how well the model knows its own uncertainty. They tested this approach on multiple real-world datasets and found consistent improvements.
What this means in practice
- •For financial analysts: Produce more reliable forecasts of multiple financial indicators by adaptively refining dependency graphs during probabilistic modeling.
- •For energy grid operators: Improve probabilistic forecasting of interconnected energy demand and supply variables by progressively adjusting dependency graphs for uncertainty.
Authors
Rui Han, Min Yang, Xu Zhang, Xinghao Yang, Wei Liu, Yongshun Gong
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.