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

PrismFlow introduces a novel Flow Matching method for time-series generation that uses Koopman-inspired dynamical experts to address spectral distortion problems in existing models. By employing residual corrections and confidence-aware expert selection, the approach achieves significant performance improvements (15.6% gain in Context-FID, 38.6% in Discriminative Score) while maintaining stability and effectiveness in low-data scenarios.

PrismFlow represents a methodological advance in generative modeling for time-series data, addressing a fundamental limitation in current Flow Matching implementations. Standard FM approaches use a single global vector-field estimator that struggles with multimodal patterns and multiscale dynamics, resulting in smoothed approximations that lose fine-grained temporal structures and high-frequency variations. The research identifies that when distinct temporal regimes pass through nearby flow states but require incompatible velocities, a monolithic estimator produces overly averaged predictions that distort spectral properties and limit mode coverage.

The solution employs a Koopman-inspired framework where multiple experts learn residual corrections in a latent space, enabling local nonlinear dynamics to be approximated through linear transitions. This decomposition allows specialized learning where each expert captures regime-specific patterns rather than forcing a single model to handle all variations. The confidence-aware Winner-Take-All objective further enhances specialization by updating only the best-aligned expert per sample, creating cleaner learning signals and preventing interference between expert gradients.

The empirical results demonstrate substantial improvements across benchmarks, with particular strength in Context-FID and Discriminative Score metrics. The method's robustness in low-data settings and effectiveness for forecasting and imputation tasks expand its practical applicability. For the broader machine learning and scientific computing communities, this work offers a template for addressing estimator-level smoothing in other domains where heterogeneous data distributions create conflicting modeling requirements. The Koopman-inspired approach may inspire similar decomposition strategies across generative modeling architectures.

• →PrismFlow introduces dynamical expert decomposition to address spectral distortion in Flow Matching time-series generation models.
• →The method achieves 15.6% improvement in Context-FID and 38.6% in Discriminative Score over existing approaches.
• →Confidence-aware Winner-Take-All training encourages specialized learning while preserving Flow Matching stability guarantees.
• →The approach demonstrates robustness in low-data regimes and effectiveness for both forecasting and imputation tasks.
• →Koopman-inspired latent space design enables linear approximation of complex nonlinear temporal dynamics.