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This research introduces DiffDiff, a novel framework that embeds predictability asymmetry directly into the diffusion trajectory for time series forecasting. By making the forward operator step-dependent and utilizing differential history information, the model focuses generative effort on uncertain components while preserving compatibility with existing samplers. The approach demonstrates improved performance across multiple benchmarks by effectively distinguishing between continuity-anchored content and residual uncertainty.
Differencing the Diffusion Trajectory toward Uncertain Components for Time Series Forecasting
arXiv:2607.22599v1 Announce Type: new Abstract: Diffusion models have become a widely used framework for probabilistic time series forecasting, modeling the distribution of future values given an observed history. In time series forecasting, however, the future continues the observed history, creating an asymmetry the standard diffusion process leaves unaddressed, with slowly-varying content largely determined by the observed continuity while higher-frequency dynamics carry most of the residual uncertainty. Existing diffusion-based forecasters decouple this asymmetry through an external rule before generation, leaving the corruption trajectory blind to which parts of the target the history can already anchor. We propose DiffDiff, a diffusion framework that embeds this predictability asymmetry into the diffusion trajectory itself, so that a single end-to-end diffusion process becomes aware of which parts of the target the history can already anchor. DiffDiff makes the forward operator step-dependent so that the noisy intermediate state progressively shifts from the target itself toward its second-order differenced structure, while a conditioning pathway supplies the denoiser with both value-domain and differential history information balanced by a stage-adaptive gate at each diffusion step. The terminal distribution approaches a standard Gaussian, preserving compatibility with existing samplers. On seven benchmarks across four prediction horizons, DiffDiff outperforms six diffusion baselines, and our analysis confirms that DiffDiff concentrates the diffusion's generative effort on the most uncertain components of the target while relieving it from rebuilding the history-anchored content.
Abstract:Diffusion models have become a widely used framework for probabilistic time series forecasting, modeling the distribution of future values given an observed history. In time series forecasting, however, the future continues the observed history, creating an asymmetry the standard diffusion process leaves unaddressed, with slowly-varying content largely determined by the observed continuity while higher-frequency dynamics carry most of the residual uncertainty. Existing diffusion-based forecasters decouple this asymmetry through an external rule before generation, leaving the corruption trajectory blind to which parts of the target the history can already anchor. We propose DiffDiff, a diffusion framework that embeds this predictability asymmetry into the diffusion trajectory itself, so that a single end-to-end diffusion process becomes aware of which parts of the target the history can already anchor. DiffDiff makes the forward operator step-dependent so that the noisy intermediate state progressively shifts from the target itself toward its second-order differenced structure, while a conditioning pathway supplies the denoiser with both value-domain and differential history information balanced by a stage-adaptive gate at each diffusion step. The terminal distribution approaches a standard Gaussian, preserving compatibility with existing samplers. On seven benchmarks across four prediction horizons, DiffDiff outperforms six diffusion baselines, and our analysis confirms that DiffDiff concentrates the diffusion's generative effort on the most uncertain components of the target while relieving it from rebuilding the history-anchored content.
Artificial Intelligence (cs.AI)
arXiv:2607.22599 [cs.AI]
(or arXiv:2607.22599v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2607.22599 Focus to learn more arXiv-issued DOI via DataCite
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