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

• URL: http://arxiv.org/abs/2603.10785v1
• Date: Wed, 11 Mar 2026 13:56:53 GMT
• Title: The Quadratic Geometry of Flow Matching: Semantic Granularity Alignment for Text-to-Image Synthesis
• Abstract summary: We analyze the optimization dynamics of generative fine-tuning.<n>Motivated by this insight, we propose Semantic Granularity Alignment (SGA), using Text-to-Image synthesis as a testbed.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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