# Adams Bashforth Moulton Solver for Inversion and Editing in Rectified Flow arXiv: https://arxiv.org/abs/2503.16522 ยท HTML: https://mlsanity.com/paper/2503.16522/ ## Key facts - Cited by 10 papers in the map (data through 14 Oct 2026). - Placed in Image generation, text-to-image and editing, one of 14 directions in Diffusion models. - Builds on 42 of its 48 references that are in the map. - First posted on arXiv 17 Mar 2025. ## Placed in - Diffusion models / [Image generation, text-to-image and editing](https://mlsanity.com/diffusion/image-generation-text-to-image-and-editing/) ## Builds on (most cited first, 30 of 42) - [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021) - [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020) - [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021) - [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018) - [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020) - [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022) - [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022) - [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022) - [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023) - [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024) - [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022) - [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022) - [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022) - [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022) - [Plug-and-Play Diffusion Features for Text-Driven Image-to-Image Translation](https://mlsanity.com/paper/2211.12572/) (2022) - [MasaCtrl: Tuning-Free Mutual Self-Attention Control for Consistent Image Synthesis and Editing](https://mlsanity.com/paper/2304.08465/) (2023) - [DiffEdit: Diffusion-based semantic image editing with mask guidance](https://mlsanity.com/paper/2210.11427/) (2022) - [Zero-shot Image-to-Image Translation](https://mlsanity.com/paper/2302.03027/) (2023) - [Taming Rectified Flow for Inversion and Editing](https://mlsanity.com/paper/2411.04746/) (2024) - [Negative-prompt Inversion: Fast Image Inversion for Editing with Text-guided Diffusion Models](https://mlsanity.com/paper/2305.16807/) (2023) - [Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration](https://mlsanity.com/paper/2303.11435/) (2023) - [Semantic Image Inversion and Editing using Rectified Stochastic Differential Equations](https://mlsanity.com/paper/2410.10792/) (2024) - [ReNoise: Real Image Inversion Through Iterative Noising](https://mlsanity.com/paper/2403.14602/) (2024) - [RAVE: Randomized Noise Shuffling for Fast and Consistent Video Editing with Diffusion Models](https://mlsanity.com/paper/2312.04524/) (2023) - [Stable Flow: Vital Layers for Training-Free Image Editing](https://mlsanity.com/paper/2411.14430/) (2024) - [A Picture is Worth More Than 77 Text Tokens: Evaluating CLIP-Style Models on Dense Captions](https://mlsanity.com/paper/2312.08578/) (2023) - [Improving the Training of Rectified Flows](https://mlsanity.com/paper/2405.20320/) (2024) - [Inversion-Free Image Editing with Natural Language](https://mlsanity.com/paper/2312.04965/) (2023) - [PeRFlow: Piecewise Rectified Flow as Universal Plug-and-Play Accelerator](https://mlsanity.com/paper/2405.07510/) (2024) - [FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing](https://mlsanity.com/paper/2412.07517/) (2024) ## Built on by (most cited first, 10 of 10) - [DNAEdit: Direct Noise Alignment for Text-Guided Rectified Flow Editing](https://mlsanity.com/paper/2506.01430/) (2025) - [QR-LoRA: Efficient and Disentangled Fine-tuning via QR Decomposition for Customized Generation](https://mlsanity.com/paper/2507.04599/) (2025) - [SteerFlow: Steering Rectified Flows for Faithful Inversion-Based Image Editing](https://mlsanity.com/paper/2604.01715/) (2026) - [Free Lunch for Stabilizing Rectified Flow Inversion](https://mlsanity.com/paper/2602.11850/) (2026) - [Predict to Skip: Linear Multistep Feature Forecasting for Efficient Diffusion Transformers](https://mlsanity.com/paper/2602.18093/) (2026) - [MusRec: Zero-Shot Text-to-Music Editing via Rectified Flow and Diffusion Transformers](https://mlsanity.com/paper/2511.04376/) (2025) - [LimeCross: Context-Conditioned Layered Image Editing with Structural Consistency](https://mlsanity.com/paper/2605.10319/) (2026) - [Wavelet-Guided Semantic Signal Compensation for Inversion-Free Image Editing](https://mlsanity.com/paper/2607.02421/) (2026) - [LaCache: Exact Caching and Precision-Adaptive Inference for Diffusion Large Language Models](https://mlsanity.com/paper/2607.16339/) (2026) - [CAT-Flow: Curvature-Adaptive sTeps for Flow Matching](https://mlsanity.com/paper/2609.01746/) (2026) ## Abstract (arXiv) 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.