PrismFlow: Residual Dynamics for Flow Matching in Time-Series Generation

Generating high-quality time-series data is challenging because real-world signals often exhibit multimodal patterns and multiscale dynamics, including oscillations and high-frequency variations. Flow Matching (FM) offers an efficient alternative to diffusion models, but practical implementations typically rely on a single finite-capacity global vector-field estimator. In such heterogeneous temporal distributions, distinct regimes may pass through nearby flow states while requiring incompatible conditional velocities. A monolithic estimator trained with the standard $\ell_2$ velocity-matching objective may therefore learn an overly smoothed approximation of the local transport field. This estimator-level smoothing can attenuate branch-specific dynamics, leading to spectral distortion and poor mode coverage. To address this, we propose PrismFlow, a new FM method with Koopman-inspired dynamical experts. Each expert learns residual corrections in a latent space where local nonlinear temporal evolution can be approximated by linear transitions. We further propose a confidence-aware Winner-Take-All (WTA) objective that updates only the expert best aligned with each sample while masking gradients to the others, encouraging mode-specific specialization. During sampling, the selected expert adds a residual dynamical correction to the global transport field, preserving FM stability while recovering fine-grained and high-frequency temporal structures. Across various benchmarks, PrismFlow effectively mitigates the spectral contraction in standard FM and achieves state-of-the-art performance, with a 15.6\% gain in Context-FID and a 38.6\% improvement in Discriminative Score, while remaining robust in low-data settings and effective for forecasting and imputation.