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

2026-05-22

AI Summary

Existing flow matching methods struggle to capture the local dynamics of multimodal, multiscale time series due to their reliance on a single global vector field, often resulting in spectral distortions and insufficient mode coverage. To address this, we propose PrismFlow, which introduces a Koopman-inspired mixture-of-experts mechanism that models local nonlinear dynamics via linear approximations in latent space. PrismFlow employs a confidence-aware winner-takes-all (WTA) strategy to specialize experts and applies residual dynamic corrections to the global transport field. This approach effectively preserves high-frequency details, enhances multimodal generation capabilities, and maintains flow matching stability. Experimental results demonstrate that PrismFlow achieves state-of-the-art performance across multiple benchmarks, improving Context-FID by 15.6% and discriminator scores by 38.6%, while showing robustness in low-data regimes as well as forecasting and imputation tasks.

Abstract

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.

Problem

• time-series generation
• flow matching
• multimodal dynamics
• spectral distortion
• mode coverage

Innovation

• Flow Matching
• Time-Series Generation
• Koopman Dynamics
• Residual Correction
• Winner-Take-All