E-Flow: Energy-Guided Flow Matching for Structure-Preserving Image Style Transfer

Reference-based image style transfer aims to reproduce style appearance while preserving content structure. The task remains an underdetermined multi-constraint problem where many intermediate states are plausible but only some are compatible with both content and style. Existing diffusion-based methods lack an explicit scalar criterion to rank these states, and standard Flow Matching, though providing source-to-target geometry, only regresses a coordinate-wise velocity field without scoring state compatibility or coupling all coordinates through a shared objective. In this paper, we propose Energy-Guided Flow Matching (E-Flow) for structure-preserving image style transfer. We introduce a time-dependent energy head that outputs a scalar compatibility energy, and then parameterize the transport field as its negative input gradient, coupling all coordinates through one shared landscape. Thereinto, Flow Matching supplies the geometry, while the energy determines the trajectory. To make the energy discriminative, a local contrastive divergence objective compares the correctly paired target with local alternatives from a short Langevin chain. The stochastic noise helps escape shallow local minima, while the contrastive term forms a low-energy basin around valid stylizations. In addition, we present a discrete Meyer wavelet transform to construct complementary target branches and perform reversible coefficient-space fusion. Experiments show that E-Flow improves the style-content trade-off, yielding higher feature separation with competitive NMI. The code is provided in the supplementary materials.