Masked image modeling (MIM) has been considered as the state-of-the-art (SOTA) self-supervised learning (SSL) technique in terms of visual pretraining. The impressive generalization ability of MIM also paves the way for the remarkable success of large-scale vision foundation models. In this article, we further discuss the validity and advantages of implementing MIM techniques in the reproducing kernel Hilbert spaces (RKHSs) and we associate the analysis with a novel MIM method named R-MIM (short for RKHS-MIM). Through the careful construction of an augmentation graph and by using spectral decomposition techniques, we establish a systematic theoretical understanding between the proposed R-MIM's generalization ability and the choice of kernel function used during training. Specifically, we reach a conclusion that both of the local Lipschitz constant of the resultant R-MIM model and the corresponding expected pretraining error can have a strong composite effect on bounding downstream task error, depending on the kernel options. We demonstrate that under mild mathematical assumptions, R-MIM method is guaranteed to return a lower bound on downstream tasks in comparison to vanilla MIM techniques, such as masked autoencoder (MAE) and SimMIM. Empirical justification well corroborates our theoretical hypothesis and analysis in showing the superior generalization of the proposed R-MIM and the theoretical link to kernel choices. The code is available at: https://github.com/yurui-q/R-MIM.

Diffusion models have recently brought a powerful rev-olution in image generation. Despite showing impressive generative capabilities, most of these models rely on the current sample to denoise the next one, possibly resulting in denoising instability. In this paper, we reinterpret the iterative denoising process as model optimization and leverage a moving average mechanism to ensemble all the prior samples. Instead of simply applying moving average to the denoised samples at different timesteps, we first map the denoised samples to data space and then perform moving average to avoid distribution shift across timesteps. In view that diffusion models evolve the recovery from low-frequency components to high-frequency details, we fur-ther decompose the samples into different frequency components and execute moving average separately on each component. We name the complete approach “Moving Aver-age Sampling in Frequency domain (MASF)”. MASF could be seamlessly integrated into mainstream pre-trained dif-fusion models and sampling schedules. Extensive experi-ments on both unconditional and conditional diffusion mod-els demonstrate that our MASF leads to superior performances compared to the baselines, with almost negligible additional complexity cost.