让扩散模型自动识别时间序列中可预测与不确定部分,提升预报精度。
Differencing the Diffusion Trajectory toward Uncertain Components for Time Series Forecasting

- 设计步长依赖的前向过程,逐步将噪声状态转向二阶差分结构。
- 在七个基准上优于六种扩散基线,显著降低对历史已知部分的重复生成。
- 适合需要高精度概率预测的时间序列场景,如金融、气象建模。
扩散模型已成为概率性时间序列预测的通用框架,通过观测历史建模未来值的分布。然而,在时间序列中,未来延续了历史,造成一种不对称性:缓慢变化的内容主要由历史连续性决定,而高频动态则承载了大部分残余不确定性。现有基于扩散的预测器通过外部规则在生成前解耦这种不对称性,使去噪轨迹无法感知历史能锚定目标的哪些部分。本文提出 DiffDiff,将这种可预测性不对称性直接嵌入扩散轨迹本身,使单一端到端扩散过程能够识别历史可锚定的目标部分。DiffDiff 使前向算子具有步长依赖性,使噪声中间状态逐步从目标本身转向其二阶差分结构;同时,条件路径在每一步通过阶段自适应门控,向去噪器提供值域和差分历史信息。终端分布为标准高斯,保持与现有采样器兼容。在四个预测时长的七个基准测试中,DiffDiff 超过六种扩散基线,分析表明其将生成努力集中在目标中最不确定的成分上,同时减轻对历史锚定内容的重建负担。
原文摘要 · Abstract (English)
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.
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