Low-Pass Flow Matching

2026-06-01

AI Summary

This work addresses a key limitation of conventional flow matching methods, which employ white noise as the source distribution despite its flat spectrum being inconsistent with the frequency-decaying nature of real-world data. To better align with the spectral characteristics of natural signals, the authors propose low-pass flow matching—a novel approach that introduces, for the first time in flow matching, a time-varying spectral bias mechanism. This is achieved through operator-modulated interpolation paths that dynamically steer the generative process toward low-frequency components during evolution. Combined with an adaptive ODE solver, the method enables highly efficient sampling. Experiments on unconditional image generation tasks, such as Galaxy10, demonstrate that the proposed approach significantly reduces sampling cost while maintaining or even improving sample quality.

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 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.

Problem

• Flow Matching
• white noise
• power spectra
• frequency decay
• natural data

Innovation

• Low-Pass Flow Matching
• spectral bias
• operator-modulated interpolant
• adaptive ODE solvers
• frequency-decaying spectrum