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，因为时间上的错位可能掩盖固有的形状差异并降低聚类性能。现有方法大多将配准和聚类视为独立任务，或依赖于严格参数化假设。我们提出\textbf{NeuralFLoC}——一种完全无监督的端到端深度学习框架，用于基于神经常微分方程驱动的微分同胚流和谱聚类的联合功能配准与聚类。所提出的模型能同时学习平滑可逆的扭曲函数和聚类特定的模板，有效解耦相位与幅度变异。我们为所提出的框架建立了普适逼近保证和渐近一致性。在功能基准测试上的实验表明，该方法在配准和聚类任务中均达到最优性能，且对缺失数据、不规则采样和噪声具有鲁棒性，同时保持可扩展性。代码可访问https://anonymous.4open.science/r/NeuralFLoC-FEC8。