On Exact Editing of Flow-Based Diffusion Models

TL;DR

This paper addresses instability in flow-based diffusion editing caused by accumulated velocity errors. It introduces Conditioned Velocity Correction (CVC), a principled framework that decomposes latent evolution into structure-preserving and semantically guided components, and uses a posterior-consistent Tweedie/Empirical Bayes correction conditioned on the source prior. Through an alignment objective and a velocity-update rule, CVC achieves faithful reconstruction and smooth semantic edits, validated across PIE-Bench and multiple diffusion backbones. The approach yields higher fidelity, better semantic alignment, and more reliable editing behavior, offering inversion-free, text-guided editing with strong practical impact.

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.

Figures (4)

• Figure 1: FlowEdit vs. Conditioned Velocity Correction(CVC). The upper part illustrates FlowEdit. At each time step $t$, it derives the final latent transfer velocity by simply taking the difference between the velocities corresponding to the source and target distributions. This direct subtraction inevitably leads to cumulative velocity errors over time. The bottom part presents our proposed Conditioned Velocity Correction (CVC) framework. The core innovation of CVC is that it not only significantly reduces the computational velocity error at each step but also integrates an Absolute Error Correction mechanism across the trajectory. As depicted by the orange path, our method achieves an error-free distribution transfer, ensuring an exact and consistent editing result from the source to the target distribution.
• Figure 2: Visual results of different methods on PIE-Bench. Each method is identified at the top of its respective column, while detailed editing information appears beneath each corresponding row. CVC(ours) demonstrates significant enhancements over existing methods.
• Figure 3: Reconstruction MSE via Editing Steps
• Figure 4: Application on Style Transfer