Abstract: Current clustering methods enhance performance by jointly learning cluster-friendly representation spaces and cluster assignments.However,they remain fundamentally constrained by static embedding spaces primarily derived from pre-trained visual encoders,where cluster assignments rely on rigid metric systems(e.g.,Euclidean distance or cosine similarity) within the fixed feature space.Inspired by the stable training dynamics and conditional control capabilities of diffusion models,this paper proposes a novel semi-supervised clustering framework.Methodologically,it encodes cluster centers as learnable conditional embedding vectors and constructs a noise-prediction-error-driven generative metric function,transcending the traditional Euclidean linear separability constraints.A two-stage dynamic optimization strategy is designed,integrating supervised pre-training with semantic anchoring and unsupervised adaptation with matching losses to balance intra-cluster compactness and inter-class separabi-lity.Theoretically,based on Rademacher complexity and bounded noise-prediction assumptions,it derives an expected risk upper bound of $\mathcal{O}$(k／n) proving the asymptotic consistency of the proposed method on large-scale data and guaranteeing its generalization capability.Furthermore,it demonstrates that supervised information,through strong convexity constraints and Lipschitz continuity of the denoising network,accelerates the decay rate of the dominant error term to $\mathcal{O}$(1＼/nm_c) elucidating the compression effect of labeled data on hypothesis space complexity.Experimentally,the proposed framework achieves competitive results on benchmark datasets such as ImageNet-10,supported by ablation studies validating the efficacy of key components.

Key words: Semi-supervised learning, Prompt representation learning, Diffusion models, Generative metric methods, Clustering risk