Multidimensional (M-D) seismic data denoising can be conceptualized as an underdetermined reconstruction challenge, where the solution heavily relies on the use of image priors, with machine learning-driven prior models playing a pivotal role in the processUnder-determined inverse problem. However, constructing suitable priors has been a challenging task due to the inherent complexity of M-D seismic data. In recent years, using two-dimensional or three-dimensional deep learning (DL) methodsDeep learning (DL) to capture the intrinsic features of seismic images has become a widely adopted solution. Yet, for higher-dimensional data, especially four-dimensional prestack seismic data, these deep learning-based methods often struggle to capture the full global structure of images without flattening the data. To tackle this challenge, we introduce a novel approach called the framelet-based order-p tensor neural network (FPTNN)Framelet-Based Order- Tensor Neural Network (FPTNN). This method is developed to automatically extract priors that characterize the underlying clean M-D seismic image features, utilizing a data-driven learning process. Specifically, we redefine the order-p tensor-tensor product (t-product)Tensor-tensor product (t-product) using the framelet transformFramelet transform, which has clear advantages over the traditional Fourier transform in terms of preserving local features and handling high-dimensional data. With this revised approach, we create a unique tensor neural network framework that advances the conventional tensor neural network (tNN)Tensor neural network (t-NN) into a design optimized for handling multidimensional seismic data cleaning tasks. The key benefit of this framework is its ability to compute the order-p t-product efficiently through matrix operations in the framelet domain, leading to a significant boost in computational efficiency. Leveraging this property, we apply deep learning techniquesDeep learning (DL) to optimize the weight parameters of the transformed matrix frontal slices, further improving the model’s performance. Comprehensive experiments on both synthetic and real-world seismic datasets demonstrate that the proposed FPTNN model achieves superior denoising performance compared to current leading methods. This approach offers a fresh perspective for multidimensional seismic data denoising and shows significant promise for real-world applications.