Clustering functional data in the presence of phase variation is challenging, as temporal misalignment can obscure intrinsic shape differences and degrade clustering performance. Most existing approaches treat registration and clustering as separate tasks or rely on restrictive parametric assumptions. We present \textbf{NeuralFLoC}, a fully unsupervised, end-to-end deep learning framework for joint functional registration and clustering based on Neural ODE-driven diffeomorphic flows and spectral clustering. The proposed model learns smooth, invertible warping functions and cluster-specific templates simultaneously, effectively disentangling phase and amplitude variation. We establish universal approximation guarantees and asymptotic consistency for the proposed framework. Experiments on functional benchmarks show state-of-the-art performance in both registration and clustering, with robustness to missing data, irregular sampling, and noise, while maintaining scalability. Code is available at https://anonymous.4open.science/r/NeuralFLoC-FEC8.

翻译：在存在相位变异的情况下对功能数据进行聚类具有挑战性，因为时间上的错位会掩盖内在的形状差异并降低聚类性能。大多数现有方法将配准和聚类视为独立的任务，或依赖于限制性的参数假设。我们提出了 \textbf{NeuralFLoC}，一个完全无监督、端到端的深度学习框架，用于基于神经常微分方程驱动的微分同胚流和谱聚类的功能联合配准与聚类。该模型同时学习平滑、可逆的扭曲函数和特定于聚类的模板，有效地解耦了相位和幅度变异。我们为所提出的框架建立了通用逼近保证和渐近一致性。在功能基准测试上的实验表明，该框架在配准和聚类方面均达到了最先进的性能，并对缺失数据、不规则采样和噪声具有鲁棒性，同时保持了可扩展性。代码可在 https://anonymous.4open.science/r/NeuralFLoC-FEC8 获取。