On Exact Editing of Flow-Based Diffusion Models

TL;DR

This paper introduces Conditioned Velocity Correction (CVC), a novel framework for flow-based diffusion editing that improves the stability, fidelity, and semantic consistency of image transformations by explicitly decomposing and correcting latent velocity trajectories.

Contribution

CVC reformulates flow-based diffusion editing as a distribution transformation problem with a dual-velocity mechanism and employs Empirical Bayes inference for error correction, enhancing stability and fidelity.

Findings

CVC achieves higher fidelity in image editing tasks.

CVC provides better semantic alignment compared to previous methods.

CVC demonstrates more reliable and stable latent trajectory control.

Abstract

Recent methods in flow-based diffusion editing have enabled direct transformations between source and target image distribution without explicit inversion. However, the latent trajectories in these methods often exhibit accumulated velocity errors, leading to semantic inconsistency and loss of structural fidelity. We propose Conditioned Velocity Correction (CVC), a principled framework that reformulates flow-based editing as a distribution transformation problem driven by a known source prior. CVC rethinks the role of velocity in inter-distribution transformation by introducing a dual-perspective velocity conversion mechanism. This mechanism explicitly decomposes the latent evolution into two components: a structure-preserving branch that remains consistent with the source trajectory, and a semantically-guided branch that drives a controlled deviation toward the target distribution. The conditional velocity field exhibits an absolute velocity error relative to the true underlying distribution trajectory, which inherently introduces potential instability and trajectory drift in the latent space. To address this quantifiable deviation and maintain fidelity to the true flow, we apply a posterior-consistent update to the resulting conditional velocity field. This update is derived from Empirical Bayes Inference and Tweedie correction, which ensures a mathematically grounded error compensation over time. Our method yields stable and interpretable latent dynamics, achieving faithful reconstruction alongside smooth local semantic conversion. Comprehensive experiments demonstrate that CVC consistently achieves superior fidelity, better semantic alignment, and more reliable editing behavior across diverse tasks.