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

Zhente Zhang, Zhengwei Ni, Wei Fan

arXiv:2609.02068v1cs.LG

TL;DR

Probabilistic MTS forecasting must handle heterogeneous variable reliability while modeling uncertainty and cross-variable dependence. DynG-Diff separates unconditional joint-distribution learning from adaptive observation guidance, achieving competitive benchmark performance and robustness under corrupted observations, with inference overhead remaining a limitation.

  • Problem

    Existing diffusion forecasting methods use task-specific conditional paradigms and struggle to accommodate differing noise levels and evolutionary patterns across variables.

  • Method

    DynG-Diff freezes an unconditional diffusion backbone and uses a separately trained State-Aware Policy Network to produce variable- and timestep-specific guidance from noisy states and one-step estimates.

  • Results

    DynG-Diff achieves competitive forecasting accuracy and probabilistic performance across real-world benchmarks, including average CRPS values of 0.321 on ETTh1 and 0.395 on Appliance.

  • Takeaways & Limitations

    Dynamic local-precision guidance strengthens reliable observations while reducing interference from noisy or anomalous variables during inference.

  • Takeaways & Limitations

    Dynamic guidance increases Traffic inference time from 28.62 to 37.31 minutes, approximately 30.4%, making the current implementation better suited to offline or batch forecasting.

Abstract

from arXiv · show

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

1 Introduction

Probabilistic MTS forecasting must model stochastic, multimodal joint distributions while accommodating heterogeneous variables and their temporal coupling. DynG-Diff addresses this with separated unconditional distribution learning and adaptive variable-specific guidance, achieving competitive benchmark performance.

  • High-dimensional MTS forecasting must capture heterogeneous noise, physical characteristics, distribution shifts, and strong temporal interdependence across variables.
  • Existing conditional diffusion methods use end-to-end conditioning or deterministic trend extraction, but typically require task-specific retraining when horizons or objectives change.
  • DynG-Diff combines an unconditional diffusion backbone with state-dependent, variable-specific inference guidance without jointly retraining the backbone.
  • Its State-Aware Policy Network estimates variable reliability from noisy states and one-step denoising estimates, producing a dynamic guidance matrix interpreted as local observation precision.
  • DynG-Diff reports competitive accuracy and probabilistic performance on real-world benchmarks, supported by ablations and visualization analyses.

2 Related Work

Related work progresses from adversarial and variational generators toward diffusion models and guidance-based conditioning. DynG-Diff extends observation-likelihood guidance with separately trained, variable- and timestep-specific reliability weighting.

  • Time Series Generation: Early multivariate time-series generation explored GANs such as C-RNN-GAN, while later VAE methods modeled interpretable temporal structure and dynamics.
  • Time Series Diffusion Models: Diffusion forecasting methods include TimeGrad, CSDI, structured state-space replacements, and conditioning mechanisms for long-sequence temporal dynamics.
  • Diffusion Guidance: Classifier, classifier-free, and constraint-based guidance steer unconditional generation through auxiliary gradients, blended scores, or differentiable time-series properties.
  • Diffusion Guidance: DynG-Diff retains TSDiff’s unconditional backbone, one-step estimate, and likelihood gradient, but adds a separately trained policy network and variable- and timestep-specific matrix A_t.

3 Preliminaries

The forecasting problem separates observed history from unknown future targets and learns their conditional distribution rather than only point estimates. Diffusion denoising and observation-likelihood gradients provide the preliminary machinery for guided sampling.

  • Problem statement: A binary mask M separates known historical observations y_obs from unknown future targets y_target in multivariate series.
  • Problem statement: Probabilistic forecasting learns p_θ(y_target|y_obs) and generates samples that quantify predictive uncertainty while capturing stochasticity and cross-variable coupling.
  • Denoising Diffusion Probabilistic Models: Diffusion models add noise through a forward process and learn reverse denoising transitions with a neural network ε_θ(x_t,t).
  • Denoising Diffusion Probabilistic Models: The denoising network and reparameterized latent state yield a one-step estimate of the original data x_0 during generation.
  • Denoising Diffusion Probabilistic Models: Real-time x_0 estimation enables observation-based dynamic guidance during the diffusion generation process.
  • Observation Guidance: Posterior-score guidance combines an unconditional score with an observation-likelihood gradient, while the preliminary formulation uses a shared global scale s for all observed variables.

4 DynG-Diff: Variable-Sensitive Dynamic Guidance Diffusion

DynG-Diff separates joint-distribution learning from variable-sensitive inference guidance. A frozen unconditional diffusion backbone supplies denoising states, while a lightweight policy network converts state-dependent reliability into dynamic local precision for probabilistic observation guidance.

  • Framework Overview: DynG-Diff uses three stages: unconditional backbone pre-training, state-aware policy learning, and dynamic-guidance inference.The decoupled design preserves joint-distribution modeling while enabling variable-specific interventions during inference.
  • Framework Overview: The frozen backbone provides both an unconditional generative prior and one-step denoising estimates used to assess recovery state and variable reliability.The policy network uses the current noisy state together with the backbone estimate during diffusion.
  • State-Aware Policy Network: The policy network combines the noisy state, one-step estimate, and timestep embedding to output a non-negative guidance matrix A_t for each variable and diffusion timestep.Lightweight 1D convolutions extract temporal and cross-variable features before the prediction head normalizes the weights.
  • State-Aware Policy Network: The matrix A_t is interpreted as dynamic local precision: each element estimates inverse error tolerance under an Asymmetric Laplace observation model.This interpretation gives the guidance weights a probabilistic meaning rather than treating them as an attention mask.
  • State-Aware Policy Network: Because true intermediate reliability labels are unavailable, the policy learns from denoising residuals transformed into log-precision, normalized, and clipped into a relative confidence target.The squared error between the one-step estimate and the noise-free signal supplies the self-supervised proxy.
  • Variable-Sensitive Guidance: Conditional independence is assumed for observed variables, while cross-channel feature fusion allows each detached local precision to encode system-wide coupling and relative reliability.When A_t equals one, the formulation reduces to homogeneous observation self-guidance with one shared scale; recomputed A_t generalizes it across variables and positions.

5 Experiments

DynG-Diff is evaluated on six real-world multivariate time-series benchmarks using MSE and CRPS against representative diffusion-based probabilistic forecasting methods. Results show competitive forecasting, strong gains on heterogeneous datasets, robustness to corrupted observations, and added inference cost.

  • 5.1 Experimental setup: Six publicly available datasets span energy, economics, meteorology, and transportation, with prediction horizons of 96, 168, 336, and 720.The benchmarks include ETTh1, Exchange, Weather, Appliance, Solar, and Traffic.
  • 5.1 Experimental setup: DynG-Diff is compared with TimeGrad, CSDI, SSSD, TimeDiff, TMDM, and D3U using CRPS and MSE.CRPS evaluates the empirical predictive distribution, while MSE measures point forecasting performance.
  • 5.2 Main results: 0.321 and 0.395 are DynG-Diff’s average CRPS values on ETTh1 and Appliance, outperforming TMDM’s 0.454 and 0.574 and D3U’s 0.425 and 0.563.These results are reported for datasets characterized by complex heterogeneity.
  • 5.2 Main results: 0.190 is DynG-Diff’s lowest average CRPS on Weather, while its average MSE of 0.502 exceeds D3U and TMDM; on Solar, it ranks second across all horizons.The reported divergence indicates stronger distributional forecasting than mean-point estimation on Weather.
  • 5.2 Main results: At Traffic horizon L = 720, DynG-Diff’s MSE is 0.626 versus D3U’s 0.610, while CRPS is 0.362 versus 0.289.The paper identifies long-horizon calibration, dense reliability estimation across 862 variables, and absent sensor-topology modeling as boundaries.
  • 5.3 Ablation studies: 125.6% and 81.7% are the average MSE and CRPS degradations when guidance is removed, while homogeneous guidance worsens them by 26.1% and 14.8%.The ablation results support observation guidance and variable-sensitive weighting for the unconditional diffusion backbone.
  • 5.3 Ablation studies: Dynamic guidance produces tighter ETTh1 prediction intervals while maintaining ground-truth coverage, and its weights weaken around low-precision or anomalous channels.The visual analyses indicate that reliability varies across variables and diffusion timesteps.
  • 5.4 Robustness analysis: Under injected noise, dynamic guidance reduces unreliable-channel influence, but Weather’s MSE behavior does not imply improved probabilistic quality because CRPS remains higher.The analysis attributes this discrepancy to finite-sample mean shifts after reweighting corrupted channels.

6 Conclusion

DynG-Diff separates unconditional joint-distribution learning from variable-sensitive observation guidance during inference, using a policy network to infer reliability from noisy states and one-step estimates. Experiments show competitive performance across real-world datasets and robustness under severe noise, while future work targets broader tasks, faster sampling, and spatial dependencies.

  • 6 Conclusion: DynG-Diff separates unconditional joint-distribution learning from variable-sensitive observation guidance during inference.The framework uses a lightweight policy network to adaptively infer variable reliability from real-time noisy states and one-step denoising estimates.
  • 6 Conclusion: The policy network formulates dynamic guidance weights as local precision, strengthening guidance for high-confidence variables while suppressing anomalous-noise interference.Guided inference uses the policy outputs to calculate an observation likelihood-based gradient without retraining the backbone.
  • 6 Conclusion: Experiments demonstrate competitive performance in most scenarios, while stress tests validate robustness under severe noise.The conclusion characterizes these findings across multiple real-world datasets without claiming uniform superiority.
  • 6 Conclusion: Future work will investigate missing-value imputation, anomaly detection, faster reverse diffusion sampling, and topological structures for spatial dependencies.These directions extend task-specific guidance, accelerate sampling, and model spatial relationships among heterogeneous variables.

B.1 Unconditional Backbone Network Architecture and Training Details

The unconditional backbone learns the joint distribution of multivariate time series from noisy states and diffusion timesteps. It uses S4-based residual blocks to extract long-term dependencies, aggregate skip features, and predict the Gaussian noise at each timestep.

  • B.1 Unconditional Backbone Network Architecture and Training Details: The backbone learns the underlying joint distribution of multivariate time series as a generative prior for inference-time guidance.It is trained independently and remains unconditional during pre-training, without historical observations or forecasting labels.
  • B.1 Unconditional Backbone Network Architecture and Training Details: At each diffusion timestep, the network receives the noisy state x_t and timestep t, then predicts Gaussian noise with matching dimensions.The input and output are both defined over sequence length L and variable dimension D.
  • B.1 Unconditional Backbone Network Architecture and Training Details: The backbone and policy networks are optimized independently in the decoupled training paradigm.The trained backbone supplies one-step estimates at arbitrary diffusion timesteps for subsequent guidance.
  • B.1 Unconditional Backbone Network Architecture and Training Details: S4 residual blocks extract long-term temporal dependencies, while globally aggregated skip features are fused with residuals to produce the predicted noise.The architecture comprises feature and time mapping, temporal feature extraction, and output aggregation modules.

B.2 Asymmetric Laplace Distribution Modeling for Conditional Observation Distribution

DynG-Diff models the conditional observation distribution with an Asymmetric Laplace Distribution to represent predictive uncertainty. The policy output supplies a variable- and timestep-specific local precision used in the guidance update.

  • B.2 Asymmetric Laplace Distribution Modeling for Conditional Observation Distribution: The conditional observation distribution p(y_obs|x_t) is modeled with an Asymmetric Laplace Distribution to delineate predictive uncertainty.The distribution is parameterized by location, scale, and asymmetry parameters.
  • B.2 Asymmetric Laplace Distribution Modeling for Conditional Observation Distribution: The policy output is mapped to the inverse scale and used as the plug-in local precision during guidance.The detached policy value is held constant with respect to x_t during the local guidance update.
  • B.2 Asymmetric Laplace Distribution Modeling for Conditional Observation Distribution: The resulting observation likelihood is differentiated with respect to the noisy state to construct the guidance signal.This precision-weighted formulation supports variable-sensitive updates during inference.

C.1 Additional Comparisons of Generated Probabilistic Forecasting Intervals

Additional interval comparisons examine Exchange, Weather, Appliance, Solar, and Traffic under adjusted historical and prediction windows. Dynamic guidance produces compact intervals that cover true observations more effectively than no guidance or homogeneous scalar guidance.

  • C.1 Additional Comparisons of Generated Probabilistic Forecasting Intervals: The comparison covers probabilistic forecasting intervals on Exchange, Weather, Appliance, Solar, and Traffic, with windows adjusted for dataset sampling frequencies.The supplementary comparisons extend the earlier ETTh1 analysis across five datasets.
  • C.1 Additional Comparisons of Generated Probabilistic Forecasting Intervals: Dynamic guidance consistently generates more compact probabilistic intervals that effectively cover the true observations.The comparison is presented across subfigures for the additional datasets.
  • C.1 Additional Comparisons of Generated Probabilistic Forecasting Intervals: No-guidance intervals show significant dispersion, whereas homogeneous scalar guidance often produces overly conservative boundaries because of global trade-offs.These modes are contrasted with the variable-sensitive dynamic guidance intervals.

C.2 Panoramic Views of Spatiotemporal Consistency in the Dynamic Weight Network

Figure C.2 compares true observational precision with network-generated dynamic guidance weights across five datasets and key diffusion-denoising steps. The weights consistently show high spatiotemporal semantic consistency with true precision despite differences in variable dimensions and sampling frequencies.

  • Cross-dataset heatmap comparisons: The comparison spans five datasets with H = L = 168, covering varied variable dimensions and sampling frequencies.The datasets are ETTh1, Exchange, Appliance, Solar, and Traffic.
  • Observed consistency: Dynamic guidance weights consistently maintain high spatiotemporal semantic consistency with true observational precision across datasets.In the Traffic heatmap, true precision shows prominent horizontal band-like features associated with long-term and inherent signal-to-noise structure.
  • Cross-dataset heatmap comparisons: Figure C.2 compares true observational precision with network-generated dynamic guidance weights at key diffusion-process time steps.The heatmaps cover ETTh1, Exchange, Appliance, Solar, and Traffic.
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