Temporal Pair Consistency for Variance-Reduced Flow Matching

TL;DR

The paper introduces Temporal Pair Consistency (TPC), a novel variance-reduction technique for continuous-time generative models that improves sample quality and efficiency without altering model architecture or training procedures.

Contribution

TPC is a lightweight, estimator-level regularization method that reduces gradient variance in flow matching models, enhancing performance across multiple datasets and modern pipelines.

Findings

TPC reduces gradient variance and improves sample quality.

Achieves lower FID scores at similar or lower computational costs.

Extends seamlessly to state-of-the-art flow-based generative pipelines.

Abstract

Continuous-time generative models, such as diffusion models, flow matching, and rectified flow, learn time-dependent vector fields but are typically trained with objectives that treat timesteps independently, leading to high estimator variance and inefficient sampling. Prior approaches mitigate this via explicit smoothness penalties, trajectory regularization, or modified probability paths and solvers. We introduce Temporal Pair Consistency (TPC), a lightweight variance-reduction principle that couples velocity predictions at paired timesteps along the same probability path, operating entirely at the estimator level without modifying the model architecture, probability path, or solver. We provide a theoretical analysis showing that TPC induces a quadratic, trajectory-coupled regularization that provably reduces gradient variance while preserving the underlying flow-matching objective. Instantiated within flow matching, TPC improves sample quality and efficiency across CIFAR-10 and ImageNet at multiple resolutions, achieving lower FID at identical or lower computational cost than prior methods, and extends seamlessly to modern SOTA-style pipelines with noise-augmented training, score-based denoising, and rectified flow.