# On Exact Editing of Flow-Based Diffusion Models

arXiv: https://arxiv.org/abs/2512.24015 · HTML: https://mlsanity.com/paper/2512.24015/

## Key facts

- Cited by 1 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 49 of its 54 references that are in the map.
- First posted on arXiv 30 Dec 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 49)

- [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)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [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)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [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)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [InstructPix2Pix: Learning to Follow Image Editing Instructions](https://mlsanity.com/paper/2211.09800/) (2022)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [HunyuanVideo: A Systematic Framework For Large Video Generative Models](https://mlsanity.com/paper/2412.03603/) (2024)
- [Zero-1-to-3: Zero-shot One Image to 3D Object](https://mlsanity.com/paper/2303.11328/) (2023)
- [IP-Adapter: Text Compatible Image Prompt Adapter for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2308.06721/) (2023)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022)
- [Qwen-Image Technical Report](https://mlsanity.com/paper/2508.02324/) (2025)
- [FLUX.1 Kontext: Flow Matching for In-Context Image Generation and Editing in Latent Space](https://mlsanity.com/paper/2506.15742/) (2025)
- [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)

## Built on by (most cited first, 1 of 1)

- [Wavelet-Guided Semantic Signal Compensation for Inversion-Free Image Editing](https://mlsanity.com/paper/2607.02421/) (2026)

## Abstract (arXiv)

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.