Random noise attenuation (NA) is a key step in seismic field data processing. With the rise of artificial intelligence, deep learning (DL) algorithms are gradually introduced into seismic random noise suppression. The most commonly used DL paradigm takes mean squared error (MSE) as loss function, the default assumption is that its error term obeys independently identically distribution (IID) Gaussian, and its noise level involved preset-hyperparameters in the local area of data cannot be adjusted adaptively in the training phase. This leads to the poor generalization of deep denoiser on Non-IID noises. In this study, we propose a DL framework based on Non-IID pixel-wise Gaussian noise modeling, which integrates NA and noise level estimation into a unique Bayesian framework. The framework can adaptively characterize the noise and data distribution in the local area of noisy data through the variational inference (VI) technique, which allows the network to see more noises of varying degrees and learn effective information from them. Thus, our proposed framework called VI-Non-IID inclines to have better noise characterization and generalization capabilities, which brings better performance on seismic field NA. Furthermore, we conduct a series of experiments on seismic synthetic and field data to test the performance of two implementations of VI-Non-IID: VI-Non-IID (Unet) and VI-Non-IID denoising convolution network (DnCNN). A lot of results validate the superiority of our proposed VI-Non-IID framework. Specifically, VI-Non-IID can explicitly predict the denoised data and its corresponding noise level map simultaneously, and succeed in attenuating unknown field noises while preserving the useful seismic signals.