Hybrid diffusion-xLSTM framework for time-series prediction

Abstract Multivariate time-series forecasting is essential for decision making in energy, climate, finance, and transportation, yet existing methods struggle to jointly capture complex nonlinear dependencies, seasonal patterns, and stochastic volatility. Diffusion-based models such as TimeDiff offer strong uncertainty quantification but rely on fully connected conditioning encoders that lack explicit temporal modeling and show suboptimal seasonal performance. To address these shortcomings, we propose xFMixAR, a hybrid framework that replaces TimeDiff’s fully connected encoder with a recurrent extended long short-term memory (xLSTM) backbone that provides sequential temporal modeling, integrates a channel-wise autoregressive (AR) component for explicit linear trend modeling, and introduces an optimized Future Mixup mechanism for temporally aware data augmentation. These components are fused through a theoretically motivated additive integration and refined via a 100-step denoising diffusion process. Evaluated on eight benchmark datasets spanning 7 to 861 variables, xFMixAR achieves the lowest average rank of 1.69 across 17 models, reducing mean-squared error (MSE) by up to 20% compared to TimeDiff (e.g., 0.270 vs. 0.336 on ETTm1). Friedman–Nemenyi analysis and complementary Wilcoxon signed-rank tests indicate statistically significant performance differences ( $$p&lt;$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>&lt;</mml:mo> </mml:mrow> </mml:math> 0.01). Ablation studies reveal that Future Mixup and the AR component reduce the error by 90.7% and 31.0%, respectively, validating the complementary benefits of the hybrid architecture.