SlerpFlow: Spherical Trajectory Correction for Rectified Flow Inversion

2026-07-23

AI Summary

This work addresses reconstruction distortions and editing inconsistencies in image inversion for Rectified Flow–based models (e.g., FLUX), which stem from discretization errors of linear solvers. The authors propose SlerpFlow, a method that assumes latent-space trajectories lie on the data manifold and models them as intrinsically curved spherical paths. By leveraging spherical linear interpolation (Slerp) to correct flow velocity directions and caching the adjusted velocities, SlerpFlow enables high-precision, zero-shot inversion. Crucially, the approach treats trajectory curvature as a key mechanism for enforcing manifold constraints, achieving substantially improved reconstruction fidelity and semantic consistency in editing—using only a first-order Euler solver, without additional training or complex numerical approximations.

Abstract

Rectified-flow-based diffusion transformers, particularly FLUX, have demonstrated outstanding performance in high-quality image generation. However, achieving fast and accurate inversion--transforming images back to latent noise for faithful reconstruction and editing--remains a challenging bottleneck due to the discretization errors of linear solvers. This paper introduces SlerpFlow, a straightforward yet highly effective zero-shot approach that unlocks the full potential of FLUX for high-fidelity inversion and editing. Unlike existing approaches (e.g., RF-Solver) that rely on complex numerical approximations such as high-order Taylor expansions to correct trajectory errors, we present a geometric view based on the Manifold Hypothesis: the empirically observed trajectory curvature is not a numerical artifact, but rather serves as a necessary "centripetal force" that constrains the flow to remain on the data manifold. Guided by this insight, SlerpFlow integrates Spherical Linear Interpolation (Slerp) to rectify flow velocity directions on the hypersphere, strictly adhering to the intrinsic curvature of the latent space. Crucially, by caching the corrected velocity for subsequent steps, SlerpFlow achieves high-precision inversion while maintaining the computational efficiency of a first-order Euler solver. Extensive experiments on FLUX-based reconstruction and editing tasks demonstrate that SlerpFlow improves reconstruction fidelity and achieves stronger semantic alignment in editing without requiring additional training. Code is available at https://github.com/0answer0/SlerpFlow.

Problem

• inversion
• rectified flow
• discretization error
• image reconstruction
• latent space

Innovation

• SlerpFlow
• Rectified Flow
• Spherical Linear Interpolation
• Manifold Hypothesis
• Inversion