PolarFormer: Radial-Angular Latent Modeling for Unconditional Time Series Generation

Time series generation is essential for data augmentation and privacy-preserving analysis across many real-world domains. Recent progress in discrete token modeling (DTM) has demonstrated strong potential by transforming continuous sequences into discrete representations and performing generation in the latent space. However, existing DTM-based methods, particularly VQ-VAE based methods, suffer from imprecise manifold modeling, severe codebook collapse, and high generative complexity caused by entangled latent attributes and heuristic sequence decomposition. In this work, we propose PolarFormer, a novel framework for time series generation that addresses these limitations through a polar decomposition-based discrete representation. Specifically, we decompose continuous latent embeddings into radial and angular components, and model them using two independent codebooks, enabling a multi-layer spherical-shell latent topology that more faithfully captures the underlying data manifold. To stabilize representation learning, we reinterpret VQ-VAE quantization as a Mixture-of-Experts routing process and introduce a load-balancing loss to effectively mitigate codebook collapse. In the generative stage, we further propose a structurally decoupled generation strategy that models radial and angular token sequences jointly while leveraging their orthogonality to substantially reduce modeling complexity. Extensive experiments on multiple datasets demonstrate that PolarFormer consistently achieves state-of-the-art performance in time series generation, validating its effectiveness in representation fidelity and generative quality. Our source code has been made publicly available at https://github.com/decisionintelligence/PolarFormer