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Intelligent fault prognosis plays an essential role in ensuring the stability and safety of power systems. However, the prediction of power transformer faults encounters significant challenges, including ultra-high noise interference, imbalanced samples, and difficulties in extracting sensitive fault features. To address these problems, this paper proposes SD2SDFNet, a novel deep fusion network that utilizes statistical denoising and a dual-dimension self-attention network. The proposed approach incorporates a statistical denoising approach called successive variational mode decomposition and Cramer Von Misses (SVMD-CVM). This technique aims to decompose signals into intrinsic mode functions (IMFs) and eliminate noise from each corresponding mode. By employing SVMD-CVM, the scheme effectively mitigates the impact of noise on fault prediction. Furthermore, a dual-dimension self-attention model is developed to selectively capture salient features from different IMF and time step dimensions. This adaptive feature selection process enhances the network's ability to focus on relevant information. To integrate the extracted features from both dimensions, a deep fusion network is adopted. This fusion process combines the weighted features, resulting in a more comprehensive set of features that facilitates accurate fault prediction. Experimental evaluations conducted on hybrid-space datasets demonstrate that SD2SDFNet achieves outstanding performance in predicting inter-turn faults. The network exhibited a Mean Squared Error (MSE) of 3.25E-05 and a Relative Absolute Error (RAE) of 1.58% for sensor 1, surpassing state-of-the-art prediction methods. [ABSTRACT FROM AUTHOR]