Distribution-Aware Diffusion-LLM for Robust Ultra-Long-Term Time Series Forecasting
Authors: Falguni Ghosh, Vahid Hashemi, Bernhard Kainz
Organizations: Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, 91052, Germany · AUDI AG, Auto-Union-Straße 1, 85057 Ingolstadt, Germany · Imperial College London, London SW7 2RH, United Kingdom
Abstract
Time series forecasting is a fundamental machine learning task. Recent work has explored Large Language Models (LLMs) for this purpose due to their strong generalization, pattern recognition, and zero-shot or few-shot capabilities. Despite their suitability for long-context learning, LLMs face challenges in multimodal settings: they lack calibrated probabilistic modeling for non-text data and struggle to align heterogeneous representations. To address these issues, we propose a new framework Diffusion-LLM that integrates a conditional diffusion model into an LLM-based forecasting pipeline. This joint design enables learning the conditional distribution of future data while improving semantic alignment in a shared latent space. We evaluate Diffusion-LLM on six long-term forecasting benchmarks, including ETT, Weather, and ECL. Our method consistently outperforms existing LLM-based baseline, achieving notable gains in ultra-long-term and few-shot forecasting and demonstrating the value of distribution-aware regularization for enhancing robustness and generalization in time series LLMs.
Recent advances in Large Language Models (LLMs) have spurred cross-modal solutions for time-series forecasting. However, existing methods rely heavily on textual prompts for modality alignment-introducing nontrivial computational overhead and failing to leverage the rich spectral dynamics inherent in time-series data. To enable prompt-free, frequency-aware adaptation of frozen LLMs, we propose FM-LLM (Frequency-Enhanced Mixture-of-Experts for adapting LLMs to Time Series Forecasting), an autoregressive framework grounded in constrained asymmetric coupling. A Fourier Analysis Network (FAN)-based spectral token aligner injects structured harmonic representations directly into the frozen LLM with numerical compatibility. An asymmetric Mixture-of-Experts (MoE) decoder enforces role separation: shared experts with lightweight FAN layers reconstruct the global periodic backbone, while routed experts-restricted to standard FFNs-specialize in modeling non-periodic residual dynamics. A time-frequency hybrid loss function jointly optimizes temporal accuracy and spectral consistency, mitigating error accumulation during long-horizon autoregressive rollouts. Evaluated across eleven public benchmarks, FM-LLM achieves state-of-the-art performance on 59 out of 78 evaluation metrics. Compared to the strongest autoregressive LLM-based baseline, it delivers average improvements of 5.3% in MSE and 5.6% in MAE, with maximum gains reaching 8.0% for MSE and 8.4% for MAE. FM-LLM also demonstrates robust transferability, maintaining superior performance in 10% few-shot and zero-shot forecasting scenarios.
Long-term time series forecasting benefits from preserving global structure such as trends and seasonality. Recent LLM-based forecasters often improve accuracy through test-time scaling (e.g., iterative refinement), but these methods are computationally expensive and increasingly prone to global-shape mismatch as the prediction horizon extends. We propose SCALER, a coarse-to-fine forecasting framework that first employs a lightweight Transformer tailored to long-term shape modeling to predict a coarse representation of future dynamics. This predicted shape then serves as a compact guide for an LLM to perform test-time scaling via iterative coarse-to-fine residual token refinement, while processing substantially fewer tokens at each step. By guiding refinement with an explicit future-shape prediction, SCALER reduces reliance on long description prompts, and its fixed-step refinement avoids costly reward-model-based selection, further lowering computational overhead. Experimental results demonstrate that SCALER outperforms strong forecasting baselines in long-term, short-term and zero-shot forecasting while significantly reducing the inference cost associated with scaled LLM for time series forecasting. Code: https://github.com/xuanmay2701/SCALER.
Large Language Models (LLMs) have recently demonstrated impressive potential for time series forecasting. However, existing methods predominantly rely on passive modality alignment or static task reprogramming, which often fail to capture fine-grained, non-stationary temporal patterns or to adapt to nuanced task intents. In this paper, we propose Instruction-aware Active Probing (InA-Probe), which shifts the paradigm from passive alignment toward an active, instruction-driven probing mechanism. Specifically, we design a Multi-Level Instruction Injection mechanism that enriches the model with both global task objectives and fine-grained, patch-level semantic priors. Building on this, an Adaptive Query Generation module produces sample-specific probes that are dynamically modulated by the temporal context. These probes are then refined through a dual-stage attention process: they first internalize task-specific intents via Instruction-Aware Self-Attention, and subsequently interrogate the projected temporal representations through Temporal Cross-Attention to extract salient patterns. Comprehensive experiments on seven real-world benchmarks show that InA-Probe consistently outperforms state-of-the-art deep learning and LLM-based baselines, excelling in both one-for-all generalization and zero-shot transfer while reducing forecasting error by up to 37% in challenging cross-domain scenarios. Ablation studies further confirm that the synergy between adaptive querying and fine-grained instructions is key to unlocking the reasoning power of LLMs for complex time series.