The Quadratic Geometry of Flow Matching: Semantic Granularity Alignment for Text-to-Image Synthesis

TL;DR

This paper introduces a geometric perspective on flow matching in generative models, revealing how neural tangent kernels influence training dynamics, and proposes Semantic Granularity Alignment to improve text-to-image synthesis.

Contribution

It provides a novel geometric analysis of flow matching optimization dynamics and introduces SGA, a method to enhance training efficiency and output quality in text-to-image models.

Findings

SGA accelerates convergence in text-to-image synthesis.

SGA improves structural integrity of generated images.

Geometric analysis reveals neural tangent kernel's role in training dynamics.

Abstract

In this work, we analyze the optimization dynamics of generative fine-tuning. We observe that under the Flow Matching framework, the standard MSE objective can be formulated as a Quadratic Form governed by a dynamically evolving Neural Tangent Kernel (NTK). This geometric perspective reveals a latent Data Interaction Matrix, where diagonal terms represent independent sample learning and off-diagonal terms encode residual correlation between heterogeneous features. Although standard training implicitly optimizes these cross-term interferences, it does so without explicit control; moreover, the prevailing data-homogeneity assumption may constrain the model's effective capacity. Motivated by this insight, we propose Semantic Granularity Alignment (SGA), using Text-to-Image synthesis as a testbed. SGA engineers targeted interventions in the vector residual field to mitigate gradient conflicts. Evaluations across DiT and U-Net architectures confirm that SGA advances the efficiency-quality trade-off by accelerating convergence and improving structural integrity.