Bridging Diffusion and Autoregression for Flexible Time Series Synthesis

Synthetic time series generation is critical for data augmentation, privacy-preserving sharing, and simulation. Autoregressive models extend to arbitrary horizons but suffer compounding errors, while diffusion models achieve high fidelity through bidirectional refinement only at fixed lengths. We propose **Horizon Diffusion**, a unified framework that resolves this tension by decomposing generation into variable-length *horizon blocks* produced autoregressively across blocks yet jointly denoised within each block. Two innovations make this hybrid practical: *Horizon-Causal Attention*, a structured mask that simultaneously preserves cross-block causality and within-block bidirectional refinement, and the *Block Size Curriculum*, a deterministic Warmup–Stable–Decay schedule that fluidly transitions training from full-sequence diffusion to block-wise autoregressive generation. Our method consistently outperforms strong baselines on fidelity, diversity, and downstream utility, and remains stable when sequence length scales by $4\times$ beyond training from a single trained model. Code is available at Supplementary Material.