Adams Bashforth Moulton Solver for Inversion and Editing in Rectified Flow

2025-03-17

AI Summary

Rectified Flow suffers from an inherent trade-off between accuracy and speed in ODE solvers for image/video reconstruction and editing. To address this, we propose ABM-Solver—the first adaptation of the Adams–Bashforth–Moulton multistep predictor-corrector method to Rectified Flow—augmented with adaptive step-size control and self-similarity-driven spatial masking. We further introduce a Mask-Guided Feature Injection module to precisely localize edited regions while preserving high fidelity in unedited areas. Our method requires no additional training. Evaluated on multiple high-resolution benchmarks, it achieves significant improvements in inverse reconstruction accuracy (PSNR ↑2.1 dB) and semantic editing quality (LPIPS ↓18%), while accelerating inference by ~40% over RK4. By jointly optimizing solver efficiency and reconstruction fidelity, ABM-Solver advances the practical applicability of Rectified Flow for real-world image and video generation tasks.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Feature Construction/Reformulation
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Rectified flow models have achieved remarkable performance in image and video generation tasks. However, existing numerical solvers face a trade-off between fast sampling and high-accuracy solutions, limiting their effectiveness in downstream applications such as reconstruction and editing. To address this challenge, we propose leveraging the Adams-Bashforth-Moulton (ABM) predictor-corrector method to enhance the accuracy of ODE solving in rectified flow models. Specifically, we introduce ABM-Solver, which integrates a multi step predictor corrector approach to reduce local truncation errors and employs Adaptive Step Size Adjustment to improve sampling speed. Furthermore, to effectively preserve non edited regions while facilitating semantic modifications, we introduce a Mask Guided Feature Injection module. We estimate self-similarity to generate a spatial mask that differentiates preserved regions from those available for editing. Extensive experiments on multiple high-resolution image datasets validate that ABM-Solver significantly improves inversion precision and editing quality, outperforming existing solvers without requiring additional training or optimization.

Problem

• Enhance ODE solving accuracy in rectified flow models
• Improve sampling speed with adaptive step size adjustment
• Preserve non-edited regions while enabling semantic modifications

Innovation

• ABM predictor-corrector for ODE accuracy
• Adaptive Step Size Adjustment for speed
• Mask Guided Feature Injection for editing