## 1 Introduction
However, diffusion models, which focus on predicting the incremental noise introduced during each iteration, face challenges when a fixed amount of noise is applied uniformly across the dataset. This can cause some samples to degrade more rapidly than others, introducing instability during training and resulting in errors in the predicted data outcomes [56; 57; 58; 59]. Furthermore, if it involves the continuous generation of signal data in the deep future based on partially known data, the error of each generation and the prediction result of the model will accumulate in the data prediction process, which is fatal for deep future data prediction tasks [60; 61; 62; 63]. This requires using a method to restore the data predicted in each recurrence by the guided diffusion model to ensure that it provides accurate known data for the next recurrence. Over the past five years, deep learning is witnessing a remarkable revival, largely fueled by the emergence and widespread adoption of transformer-based architectures [64; 65; 66; 67]. The transformer-based methods have shown impressive performance in pixel matrix data restoration tasks, such as pixel matrix data super-resolution. This study added a transformer-based data restoration architecture in the prediction process, which can restore the missing pixels in the predicted data, and provide higher quality known data for the next recurrence in the prediction process. To conclude, the transformer-based data restoration architecture significantly contributes to the efficacy of guided diffusion models in predicting deep-future FEMR signal time-frequency data, which can realize the FEMR signal super prediction. This study introduces a novel guided diffusion model with a transformer-based framework that can predict the FEMR signal in the deep future through a minimal amount of known FEMR signal and an auxiliary model to recognize rock burst precursor characteristics. Our methodology consists of a two-stage process, as illustrated in Figure 1, which outlines the framework's schematic. Initially, we employ a guided diffusion model integrated with a transformer to forecast FEMR signals over an extended future period. Subsequently, a transformer-based auxiliary model is utilized to identify the precursor characteristics of rock bursts within the FEMR signals. This approach enables the prediction of FEMR signals up to 360 h (15 days) into the future using only 12 h of known signal data. As a result, the time advance for rock burst early warning, as well as the precision of precursor characteristic identification, have been significantly enhanced. Figure 1: Description of workflow. (**a**) Window sliding operation: the data range of the window selection slides from \(x_{t-2}\sim x_{t-1}\) (\(x_{t-1}\sim x_{t}\)) to \(x_{t-1}\sim x_{t}\) (\(x_{t}\sim x_{t+1}\)); the data range of the time–frequency data slides from \(x_{t-2}\sim x_{t}\) (\(x_{t-1}\sim x_{t+1}\)) to \(x_{t-1}\sim x_{t+1}\) (\(x_{t}\sim x_{t+2}\)). (**b**) Add Gaussian noise to the ground truth time–frequency data that needs to be predicted; inputs: the known part of the time–frequency data and pure Gaussian noise; network architecture of guided diffusion model with transformer; (**c**) outputs: time–frequency data in the \(x_{t-1}\sim x_{t+1}\) time range predicted by guided diffusion model with transformer; (**d**) inputs: summary of time–frequency data prediction results of the guided diffusion model with transformer; and (**e**) outputs: the auxiliary model recognition results of rock burst precursor characteristics.