Low-Pass Flow Matching

Francesco M. Ruscio, T. Konstantin Rusch

Keywords: Flow matching, autocorrelated noise, spectral bias

TL;DR: We introduce a spectral bias in flow matching to better match the data’s spectral content, while preserving the source distribution’s spectral structure.

Abstract: Flow Matching typically relies on white noise sources, a choice often misaligned with the power spectra of natural data, which tend to decay with frequency. To address this, we introduce $\textbf{Low-Pass Flow Matching}$, a variant of Flow Matching based on an operator-modulated interpolant. This formulation induces a time-varying spectral bias that transitions from the source spectrum to a frequency-decaying bias as the path approaches the data. We validate our method on unconditional image generation tasks, including the scientific Galaxy10 dataset. Empirically, we show that our method is particularly effective when paired with adaptive ODE solvers, where it improves or preserves sample quality while substantially reducing sampling cost compared to standard baselines.

Submission Number: 15