MG-TSD: Multi-Granularity Time Series Diffusion Models with Guided Learning Process This paper introduces a novel Multi-Granularity Time Series Diffusion (MG-TSD) model that leverages the inherent granularity levels within the data as given targets at intermediate diffusion steps to guide the learning process of diffusion models. The model achieves state-of-the-art predictive performance by deriving a novel multi-granularity guidance diffusion loss function and proposing a concise implementation method to effectively utilize coarse-grained data across various granularity levels. The approach does not rely on additional external data, making it versatile and applicable across various domains. Extensive experiments on real-world datasets demonstrate that the MG-TSD model outperforms existing time series prediction methods. The MG-TSD model consists of three key modules: a Multi-granularity Data Generator, a Temporal Process Module, and a Guided Diffusion Process Module. The Multi-granularity Data Generator generates multi-granularity data from observations by smoothing out the fine-grained data using historical sliding windows with different sizes. The Temporal Process Module captures the temporal dynamics of the multi-granularity time series data using RNN architecture. The Guided Diffusion Process Module generates stable time series predictions at each timestep by utilizing multi-granularity data as given targets to guide the diffusion learning process. The model introduces a novel multi-granularity guidance diffusion loss function that effectively utilizes coarse-grained data across various granularity levels. The loss function is derived by considering the intrinsic structure of time series, such as trends, which are represented by coarse-grained time series. The model ensures that the intermediate latent space retains the underlying time series structure by introducing coarse-grained targets at intermediate diffusion steps. This approach reduces variability and results in high-quality predictions. The MG-TSD model is evaluated on six real-world datasets, including Solar, Electricity, Traffic, Taxi, KDD-cup, and Wikipedia. The results show that the model achieves the lowest CRPS sum and outperforms the baseline models across all six datasets. The model's performance is further validated through ablation studies, which show that the model achieves optimal performance when the share ratio is chosen at the step where the coarse-grained samples most closely resemble intermediate states. The model also demonstrates strong performance in long-term forecasting, maintaining robustness as the prediction length increases. The MG-TSD model is implemented with a training algorithm that iteratively samples from the reverse process to reconstruct the original data. The model's inference procedure generates samples at respective granularity levels using different hidden states as conditional inputs. The model's performance is further validated through case studies, which show that the model's coarse-grained samples display a more robust capacity to capture the trends, subsequently guiding the generation of more precise fine-grained data. The model's results demonstrate its effectiveness in time series prediction, with the ability to outperform existing methods across various domains.MG-TSD: Multi-Granularity Time Series Diffusion Models with Guided Learning Process This paper introduces a novel Multi-Granularity Time Series Diffusion (MG-TSD) model that leverages the inherent granularity levels within the data as given targets at intermediate diffusion steps to guide the learning process of diffusion models. The model achieves state-of-the-art predictive performance by deriving a novel multi-granularity guidance diffusion loss function and proposing a concise implementation method to effectively utilize coarse-grained data across various granularity levels. The approach does not rely on additional external data, making it versatile and applicable across various domains. Extensive experiments on real-world datasets demonstrate that the MG-TSD model outperforms existing time series prediction methods. The MG-TSD model consists of three key modules: a Multi-granularity Data Generator, a Temporal Process Module, and a Guided Diffusion Process Module. The Multi-granularity Data Generator generates multi-granularity data from observations by smoothing out the fine-grained data using historical sliding windows with different sizes. The Temporal Process Module captures the temporal dynamics of the multi-granularity time series data using RNN architecture. The Guided Diffusion Process Module generates stable time series predictions at each timestep by utilizing multi-granularity data as given targets to guide the diffusion learning process. The model introduces a novel multi-granularity guidance diffusion loss function that effectively utilizes coarse-grained data across various granularity levels. The loss function is derived by considering the intrinsic structure of time series, such as trends, which are represented by coarse-grained time series. The model ensures that the intermediate latent space retains the underlying time series structure by introducing coarse-grained targets at intermediate diffusion steps. This approach reduces variability and results in high-quality predictions. The MG-TSD model is evaluated on six real-world datasets, including Solar, Electricity, Traffic, Taxi, KDD-cup, and Wikipedia. The results show that the model achieves the lowest CRPS sum and outperforms the baseline models across all six datasets. The model's performance is further validated through ablation studies, which show that the model achieves optimal performance when the share ratio is chosen at the step where the coarse-grained samples most closely resemble intermediate states. The model also demonstrates strong performance in long-term forecasting, maintaining robustness as the prediction length increases. The MG-TSD model is implemented with a training algorithm that iteratively samples from the reverse process to reconstruct the original data. The model's inference procedure generates samples at respective granularity levels using different hidden states as conditional inputs. The model's performance is further validated through case studies, which show that the model's coarse-grained samples display a more robust capacity to capture the trends, subsequently guiding the generation of more precise fine-grained data. The model's results demonstrate its effectiveness in time series prediction, with the ability to outperform existing methods across various domains.