DiffDiff Enhances Time Series Forecasting with Adaptive Diffusion Models.

Probabilistic time series forecasting often uses diffusion models to predict future value distributions based on historical data. However, standard diffusion processes don't inherently account for the asymmetry in time series, where slowly varying trends are largely predictable from history, while higher-frequency dynamics introduce most of the uncertainty. Existing methods typically decouple this asymmetry externally before generation, leaving the corruption process unaware of what parts of the target are already anchored by the observed history. A novel framework called DiffDiff addresses this by integrating this predictability asymmetry directly into the diffusion trajectory. Its forward operator is step-dependent, gradually shifting the noisy intermediate state from the target itself towards its second-order differenced structure. This means the model learns to concentrate its generative efforts on the most uncertain, high-frequency components of the target, rather than redundantly rebuilding predictable historical content. DiffDiff also incorporates a conditioning pathway that provides the denoiser with both value-domain and differential history information, balanced by a stage-adaptive gate at each diffusion step. This end-to-end approach allows a single diffusion process to be aware of which parts of the target are predictable. Experiments across multiple benchmarks show DiffDiff consistently outperforms other diffusion baselines, offering more efficient and accurate probabilistic time series forecasting.