Zekai Zhang

Peng Wang, Huijie Zhang, Zekai Zhang et al.

Recent empirical studies have demonstrated that diffusion models can effectively learn the image distribution and generate new samples. Remarkably, these models can achieve this even with a small number of training samples despite a large image dimension, circumventing the curse of dimensionality. In this work, we provide theoretical insights into this phenomenon by leveraging key empirical observations: (i) the low intrinsic dimensionality of image data, (ii) a union of manifold structure of image data, and (iii) the low-rank property of the denoising autoencoder in trained diffusion models. These observations motivate us to assume the underlying data distribution of image data as a mixture of low-rank Gaussians and to parameterize the denoising autoencoder as a low-rank model according to the score function of the assumed distribution. With these setups, we rigorously show that optimizing the training loss of diffusion models is equivalent to solving the canonical subspace clustering problem over the training samples. Based on this equivalence, we further show that the minimal number of samples required to learn the underlying distribution scales linearly with the intrinsic dimensions under the above data and model assumptions. This insight sheds light on why diffusion models can break the curse of dimensionality and exhibit the phase transition in learning distributions. Moreover, we empirically establish a correspondence between the subspaces and the semantic representations of image data, facilitating image editing. We validate these results with corroborated experimental results on both simulated distributions and image datasets.

Xiao Li, Zekai Zhang, Xiang Li et al.

Diffusion models, though originally designed for generative tasks, have demonstrated impressive self-supervised representation learning capabilities. A particularly intriguing phenomenon in these models is the emergence of unimodal representation dynamics, where the quality of learned features peaks at an intermediate noise level. In this work, we conduct a comprehensive theoretical and empirical investigation of this phenomenon. Leveraging the inherent low-dimensionality structure of image data, we theoretically demonstrate that the unimodal dynamic emerges when the diffusion model successfully captures the underlying data distribution. The unimodality arises from an interplay between denoising strength and class confidence across noise scales. Empirically, we further show that, in classification tasks, the presence of unimodal dynamics reliably reflects the generalization of the diffusion model: it emerges when the model generates novel images and gradually transitions to a monotonically decreasing curve as the model begins to memorize the training data.

Lianghe Shi, Meng Wu, Huijie Zhang et al.

The widespread use of diffusion models has led to an abundance of AI-generated data, raising concerns about model collapse -- a phenomenon in which recursive iterations of training on synthetic data lead to performance degradation. Prior work primarily characterizes this collapse via variance shrinkage or distribution shift, but these perspectives miss practical manifestations of model collapse. This paper identifies a transition from generalization to memorization during model collapse in diffusion models, where models increasingly replicate training data instead of generating novel content during iterative training on synthetic samples. This transition is directly driven by the declining entropy of the synthetic training data produced in each training cycle, which serves as a clear indicator of model degradation. Motivated by this insight, we propose an entropy-based data selection strategy to mitigate the transition from generalization to memorization and alleviate model collapse. Empirical results show that our approach significantly enhances visual quality and diversity in recursive generation, effectively preventing collapse.

Zhuoheng Ran, Muhammad A. A. Abdelgawad, Zekai Zhang et al.

The dramatic surge in the utilisation of generative artificial intelligence (GenAI) underscores the need for a secure and efficient mechanism to responsibly manage, use and disseminate multi-dimensional data generated by artificial intelligence (AI). In this paper, we propose a blockchain-based copyright traceability framework called ring oscillator-singular value decomposition (RO-SVD), which introduces decomposition computing to approximate low-rank matrices generated from hardware entropy sources and establishes an AI-generated content (AIGC) copyright traceability mechanism at the device level. By leveraging the parallelism and reconfigurability of field-programmable gate arrays (FPGAs), our framework can be easily constructed on existing AI-accelerated devices and provide a low-cost solution to emerging copyright issues of AIGC. We developed a hardware-software (HW/SW) co-design prototype based on comprehensive analysis and on-board experiments with multiple AI-applicable FPGAs. Using AI-generated images as a case study, our framework demonstrated effectiveness and emphasised customisation, unpredictability, efficiency, management and reconfigurability. To the best of our knowledge, this is the first practical hardware study discussing and implementing copyright traceability specifically for AI-generated content.