LEAF : Large Language Diffusion Model for Time Series Forecasting (2025)

Abstract: This paper studies the problem of time series forecasting, which aims to generate future predictions given historical trajectories. Recent researchers have applied large language models (LLMs) into time series forecasting, which usually align the time series space with textual space and output future predictions with strong autoregressive reasoning abilities. Despite their remarkable progress, these approaches usually lack an understanding of holistic temporal patterns with potential error accumulation. Towards this end, this paper proposes a simple yet effective framework that marries \underline{\text{L}} arg \underline{\text{e}} Langu \underline{\text{a}} ge Diffusion Model with time series \underline{\text{f}} orecasting (LEAF). The core of our framework is to generate future predictions with a diffusion model from a holistic view. In particular, we first introduce a tokenization module to convert time series into tokens and then adopt the language diffusion models to capture the temporal dependencies. In this way, we can transform masked time series into all the predictions with the remasking strategy. Extensive experiments on various benchmark datasets validate the effectiveness of the proposed LEAF in comparison to various baselines.

## introduction time series forecasting (tsf) assumes a critical role in various domains, including finance @xcite , healthcare (chimmula and zhang, 2020), climate science @xcite , and traffic prediction @xcite . to achieve effective tsf, traditional methods like arima @xcite and exponential smoothing (ets) @xcite have been widely adopted for capturing temporal dependencies and trend patterns in time series data. thanks to recent advances in deep learning, models such as recurrent neural networks (rnns) @xcite , convolutional neural networks * corresponding author. recently, large language models (llms), such as gpt @xcite and llama @xcite , have shown remarkable capabilities in capturing contextual dependencies in natural language. since both language and time series data involve sequential structures and rely on learned token transitions, there is a growing interest in adapting off-the-shelf llms for time series forecasting, especially under few-shot and zero-shot settings. for example, llmtime encodes time series data into sequences of numerical tokens and formulates tsf as a next-token prediction task @xcite . autotimes projects time series data into the latent space of language tokens and generates future predictions in an autoregressive manner @xcite . lstprompt further decomposes tsf into short-and long-term subtasks and formalizes the prediction into the chain-of-thought process @xcite . despite the success of these llm-based methods for tsf, we argue that the autoregressive generation framework is not inherently aligned with the nature of time series data, primarily due to two major challenges. ❶ limited understanding of the holistic temporal patterns. future intervals in time series often exhibit coherent global patterns, such as seasonality, trends, and periodic behaviors @xcite , which cannot be effectively captured through token-by-token prediction. ❷ error propagation and lack of internal consistency. the autoregressive generation always suffers from error accumulation as each prediction relies on previous ones, leading to increasingly distorted forecasts. this disrupts the internal consistency of the predicted sequence and further hinders the ability to capture global temporal patterns accurately. these limitations naturally prompt the question: can we design a tsf framework that captures the entire future trajectory, rather than predicting it step-bystep in an autoregressive manner? diffusion models have emerged as an alternative to traditional autoregressive generative frameworks. originally introduced for image generation @xcite , diffusion models iteratively transform random noise into structured data via injecting noise in a forward process and learning to reverse it to recover the original distribution. in tsf tasks, diffusion models provide a key advantage over autoregressive methods by learning and predicting the entire trajectory simultaneously @xcite @xcite . llada provides an initial attempt at the large language diffusion model, though it still remains limited to tsf @xcite . therefore, the use of diffusion models for zero-shot tsf with llms presents a promising yet largely unexplored direction. towards this end, we propose a simple yet effective approach large language diffusion model for time series forecasting (leaf), which leverages a masked diffusion model incorporating a discrete random masking process along with a mask predictor to approximate the reverse process. specifically, given the time series input, a dedicated tokenization module is first employed to transform the raw data into a sequence of discrete tokens, thereby enabling effective interaction with the llms. then, a diffusion framework is employed to guide the llms' distribution, constructing a forward masking and a subsequent reverse process to capture temporal dependencies. for the inference phase, starting with the fully masked time series input, we discretize the reverse process and apply a confidence-based remasking strategy for the iterative tsf. the contributions of this paper are as follows: ❶ new perspective. we are the first to introduce the large language diffusion framework for tsf task, which captures the entire temporal trajectory and dependencies of time series data without relying on traditional autoregressive methods. ❷ in-depth analysis. we formalize the model distribution through a forward masking process followed by a reverse process, and provide an in-depth analy-sis for the inference phase initialized from the fully masked input in tsf. ❸ state-of-the-art performance. we conduct extensive experiments on several publicly available time series datasets and experimental results show that our leaf significantly outperforms existing comparative methods. ## the proposed leaf in this paper, we first formalize the problem setting and then introduce the details of our proposed leaf, which investigates the large language diffusion framework for zero-shot tsf. in particular, our framework consists of three components. given the time series data, it is recognised as a string of numerical digits, and each digit is viewed as a discrete token. then, we define a diffusion framework via a model distribution with forward masking and subsequent reverse process. finally, for the inference phase, we employ a confidence-based remasking strategy for iteratively tsf. the overview of the framework is shown in figure 1 , with the details of each component presented as follows. ## conclusion in this paper, we present leaf, a large language diffusion framework for zero-shot time series forecasting. by integrating a denoising diffusion process with digit-level tokenization, leaf effectively captures global and holistic temporal trajectory and dependencies that are challenging for traditional autoregressive llms. extensive experi-ments across diverse benchmarks demonstrate that leaf achieves highly competitive performance, frequently surpassing both zero-shot and supervised baselines, particularly on datasets with strong periodicity. ablation and case studies further highlight the significance of percentile-based rescaling, the effectiveness of the diffusion mechanism, and the model's ability to prioritize structural and highorder information during generation.