Rectified Flow

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Rectified flow learns a time-dependent velocity field that transports simple noise distributions into data, often along straighter paths than diffusion models. Researchers improve these transports through coupling and source-distribution design, consistency training and distillation, and guidance or geometric constraints for tasks such as image editing, restoration, forecasting, and robot control. The approach is being applied across images, audio, medical data, and embodied policies, with work also studying sample complexity, optimal transport, and privacy. A central tension is how to reduce inference to very few steps while preserving fidelity, diversity, and reliable behavior under changing conditions.

Latest papers

60 papers6 papers in the last four weeks, level with the four weeks before. 0.0% of all new papers.

Jun 16, 2026

Root-Selecting Fixed-Point Inversion for Rectified Flows via Trajectory Straightness

Finding the initial noise that generates a given data sample, known as inversion, is a key component for downstream applications such as training-free image editing. Existing fixed-point inversion methods improve inversion accuracy by formulating each inversion step as a fixed-point problem, but they lack a principled mechanism for selecting among multiple fixed-point solutions that can arise in practice. We observe that different selections induce different inversion trajectories, leading to substantial variation in reconstruction and editing quality. For rectified flows, we further find that this variation is closely associated with trajectory straightness, motivating straightness as a principled selection criterion. We propose SelFix, a fixed-point inversion method that selects fixed-point solutions inducing straighter inverse trajectories while retaining convergence to an exact inverse root under standard local assumptions. Experiments on FLUX.1-dev and PIE-Bench show that SelFix improves fixed-point inversion, achieving stronger real-image reconstruction and better source-preserving prompt-based editing than prior inversion baselines. The code is available at https://github.com/seminkim/selfix.

Semin Kim, Jihwan Yoon, Seunghoon Hong

KAIST

Diffusion Model Inversion Rectified Flow Diffusion-Based Image Editing

Jun 5, 2026

Where Rectified Flows Leak: Characterising Membership Signals Along the Interpolation Path

Understanding what generative models retain from training data remains challenging, with implications for copyright and privacy. Beyond verbatim reproduction, models can encode subtler traces of their training data that never surface in their outputs yet remain exploitable. We study this regime for Rectified Flows, which are increasingly used in deployed generative systems. We analyse the interpolation path

X_λ= (1-λ)X_0 + λX_1

that defines the Rectified Flow training. We show that a gap exists between the reconstruction of train and test data that follows a bell-shaped curve over

λ

, wich accumulates during training, while the validation metrics remain stable. The signal has a maximum whose location we derive in closed form under Gaussian assumptions. We validate these predictions on both audio and images and show that the bell-shaped structure is universal, while the peak prediction holds when our assumptions are satisfied. As a proof of concept, we exploit this specific

λ

-resolved structure to perform a Membership Inference Attack, distinguishing members of the training set from non-members.

Thomas Sesmat, Gabriel Meseguer-Brocal, Geoffroy Peeters

LTCI, Télécom Paris, Institut Polytechnique de Paris, Palaiseau, France · Deezer Research, Paris, France

Data Leakage Rectified Flow Membership Inference Attacks Memorization in Generative Models Generative Modeling Flow-Based Generative Modeling

Jun 4, 2026

SB-RF: Schrödinger Bridge Rectified Flow for One-Step Robust Speech Enhancement

Generative models have shown promising results for speech enhancement (SE), but they often rely on multi-step inference, limiting low-latency deployment. We propose SB-RF, a one-step generative framework that integrates Rectified Flow (RF) with Schrödinger Bridge (SB) theory. During training, SB-RF samples intermediate states from an SB time marginal and trains a conditional velocity field with the RF velocity-matching objective. At inference, SB-RF starts from the noisy observation and applies a single Euler update. Experiments show that SB-RF achieves competitive performance among generative methods on the VoiceBank-DEMAND benchmark. To further assess performance beyond this standard setting, we evaluate SB-RF on a simulated low signal-to-noise ratio test set using an expanded training dataset. Under these conditions, SB-RF achieves superior performance over the compared baselines, supporting its potential for real-world applications.

Caixia Lu, Xueyang Lv, Penglong Hu +1

Rectified Flow Schrödinger Bridges One-Step Generative Modeling Speech Enhancement Flow-Based Generative Modeling Noise Robustness

May 29, 2026

Probabilistic Precipitation Nowcasting with Rectified Flow Transformers

Accurate weather forecasts are essential across various domains and are safety-critical in extreme weather conditions. Compared to simulation-based forecasting, data-driven approaches show greater efficiency, enabling short-term, high-resolution nowcasting. In particular, diffusion models proved effective in weather nowcasting due to their strong probabilistic foundation. However, existing methods rely on deterministic compression to reduce the complexity of high-dimensional weather data, limiting their ability to capture uncertainty in the decoding process. In this work, we introduce

\textbf{FREUD}

, a

\textbf{Fr}

ame-wise

\textbf{E}

ncoder and

\textbf{U}

nited

\textbf{D}

ecoder model based on rectified flow transformers for efficient compression of spatio-temporal weather data. Frame-wise encoding enables continuous forecast updates, while the unified video decoder ensures temporal consistency. Our uncertainty-preserving first stage allows us to capture aleatoric uncertainty via ensembling, which is particularly beneficial for extreme weather events with high decoding variability. We achieve state-of-the-art performance in precipitation nowcasting with a compact latent-space rectified flow transformer on the SEVIR benchmark and show further performance gains by model and test-time scaling. Code available here: https://github.com/CompVis/weather-rf

Johannes Schusterbauer, Jannik Wiese, Nick Stracke +2

Precipitation Forecasting Rectified Flow Probabilistic Forecasting Precipitation Nowcasting

May 29, 2026

Geometric Erasure by Contrastive Velocity Matching in Rectified Flows

While the rapid adoption of multimodal generative models offers immense potential, it has also increased the risks of harmful content synthesis, deepfakes, and copyright infringements. To address these challenges, concept erasure has emerged as a prospective safeguard. However, as the field gradually transitions from U-Net-based diffusion models to Rectified Flow Transformers, erasure research has struggled to keep pace. In this work, we introduce GEM, a simple but highly effective erasure framework for Rectified Flow models. As part of our contribution, we establish a principled bridge between trajectory-based unlearning grounded in Generative Flow Networks and classic teacher-guided erasure: we translate trajectory-based signals into a teacher-guided flow-matching setup that unifies the strengths of both paradigms. Concretely, a teacher provides complementary attraction and repulsion signals that we combine into a single geometric guidance objective, yielding targeted suppression of unwanted concepts while preserving benign generation.

Jonas Henry Grebe, Tobias Braun, Anna Rohrbach +1

Technical University of Darmstadt & hessian.AI, Germany.

Contrastive Flow Matching Rectified Flow Flow-Based Generative Modeling Concept Erasure

May 25, 2026

AdvantageFlow: Regularized Advantage-Weighted RL in Flow Models

We present AdvantageFlow, a forward-process reinforcement learning (RL) algorithm for rectified flow models. The algorithm minimizes an advantage-weighted prediction loss, which maximizes reward, regularized by the rollout policy, which convexifies the objective and makes its optimization stable. Our objective can be viewed as fitting a local reward-improving target distribution. The rollout regularization arises as a variance reduction step. We evaluate AdvantageFlow empirically on text-to-image generation with Stable Diffusion 3.5 Medium and FLUX.1, and compare it to both forward- and reverse-process RL algorithms.

Branislav Kveton, Anup Rao, Subhojyoti Mukherjee +2

Adobe Research

Rectified Flow RL for Image Generation Flow-Based Generative Modeling RL for Generative Models RL for Flow Matching Models

May 22, 2026

VDE: Training-Free Accelerating Rectified Flow Model via Velocity Decomposition and Estimation

Though rectified flow models have achieved remarkable performance in image, video, and 3D generation, their practical deployments are challenged by slow inference speeds. Prior acceleration methods reuse cached features from previous steps, which neglects the growing mismatch between static caches and the evolving input, leading to reduced output fidelity. This work proposes Velocity Decomposition and Estimation (VDE), a training-free acceleration method that shifts the paradigm from caching-and-reusing to decomposing-and-estimating. Specifically, VDE decomposes the model's velocity into components parallel and orthogonal to the input, exploiting their temporal predictability and directional stability for precise, input-adaptive estimation. To prevent error accumulation, it periodically anchors the model's state via full forward passes. Extensive experiments on image and video generation tasks demonstrate that VDE achieves substantial acceleration with minimal loss in visual quality. Notably, VDE accelerates Flux by 3.22 times and achieves an LPIPS of 0.069 on Qwen-Image, outperforming the best baseline with a 52.2% reduction.

Junwen Tan, Jinglin Liang, Hongyuan Chen +1

South China University of Technology

Rectified Flow Image Generation Video Generation Diffusion Model Inference Acceleration

May 18, 2026

Divergence-Suppressing Couplings for Rectified Flow

The promise of Rectified Flow rests on producing self-generated couplings whose trajectories are straight, or nearly so. In practice, trajectories generated by the base flow model can bend and intertwine, and the resulting coupling inherits this distortion. In this paper, we identify that such trajectory entanglement is often associated with regions of nonzero divergence in the learned velocity field, where local expansion or contraction distorts trajectories and steers particles away from their ideal endpoints. We then propose divergence-suppressing couplings for Rectified Flow, an offline correction that attenuate the divergent component of the learned velocity during coupling generation. The correction is paid only once per coupling pair and amortized over training, so deployment runs plain Euler at identical wall-clock cost to standard Rectified Flow. Empirically, this offline modification yields consistent improvements on 2D synthetic benchmarks and on image generation.

Yimeng Min, Carla P. Gomes

Department of Computer Science Cornell University Ithaca, NY 14850

Rectified Flow Image Generation Generative Modeling

May 16, 2026

Accelerating Rectified Flow Models via Trajectory-Aware Caching

Diffusion and rectified flow (RF) models generate high-fidelity images and videos, but their iterative velocity-field evaluations are computationally expensive. Existing caching methods accelerate sampling by skipping timesteps, yet their coarse approximations introduce accumulated errors over long skip intervals and degrade quality under aggressive acceleration. We propose TACache (Trajectory-Aware Cache), a training-free acceleration framework following a skip-then-compensate paradigm. TACache performs an orthogonal decomposition of discrete velocity acceleration along the RF trajectory into a parallel component and an orthogonal residual, isolating the magnitude and directional sources of per-step approximation error. The framework operates in two stages: offline, cumulative variation thresholds on the magnitude and direction indicators yield the skip schedule and bound how far each skip interval may extend; online, at each skipped step the offline statistics are combined with the sample's historical orthogonal direction to reconstruct the skipped velocity without additional model evaluations. Experiments on BAGEL, FLUX.1-dev, and Wan2.1-1.3B show that TACache achieves up to 4.14 speedup on text-to-image generation and 2.11 speedup on text-to-video generation, with consistent improvements over prior cache-based methods on all reference-based fidelity metrics. Code will be released soon.

Xiao Liu, Kai Liu, Naiyang Guan +5

Shanghai Jiao Tong University, Shanghai, China · Academy of Military Science, Beijing, China · Huawei Technologies Ltd, Shenzhen, China

Video Diffusion Models Rectified Flow Diffusion Model Caching Diffusion Model Inference Acceleration T2I Diffusion Models

May 13, 2026

PVRF: All-in-one Adverse Weather Removal via Prior-modulated and Velocity-constrained Rectified Flow

Adverse weather removal (AWR) in real-world images remains challenging due to heterogeneous and unseen degradations, while distortion-driven training often yields overly smooth results. We propose PVRF, a unified framework that integrates zero-shot soft weather perceptions with velocity-constrained rectified-flow refinement. PVRF introduces an AWR-specific question answering module (AWR-QA) that uses frozen vision--language models (VLMs) to estimate soft probabilities of weather types and low-level attribute scores. These perceptions condition restoration networks via attribute-modulated normalization (AMN) and weather-weighted adapters (WWA), producing an anchor estimate for refinement. We then learn a terminal-consistent residual rectified flow with perception-adaptive source perturbation and a terminal-consistent velocity parameterization to stabilize learning near the terminal regime. Extensive experiments show that PVRF improves both fidelity and perceptual quality over state-of-the-art baselines, with strong cross-dataset generalization on single and combined degradations. Code will be released at https://github.com/dongw22/PVRF.

Wei Dong, Han Zhou, Terry Ji +6

McMaster University · Shanghai Jiao Tong University

Rectified Flow All-in-One Image Restoration

May 13, 2026

Coreset-Induced Conditional Velocity Flow Matching

We propose Coreset-Induced Conditional Velocity Flow Matching (CCVFM), a generative model that augments hierarchical rectified flow with a data-informed source distribution. Hierarchical flow matching models the full conditional velocity law in velocity space, but its inner flow is asked to transport isotropic Gaussian noise to a multimodal target velocity distribution from scratch. Our key observation is that this inner source can be replaced by a closed-form surrogate built from a coreset of the target. CCVFM first compresses the target into weighted atoms using an entropic Sinkhorn coreset and lifts them to a Gaussian mixture. The induced conditional velocity law is then a closed-form Gaussian mixture that can be sampled without a learned neural sampler. A lightweight correction flow, trained from this exact surrogate source, then refines the remaining surrogate-to-target residual rather than learning an entire noise-to-data map. We prove that the surrogate transport cost equals the target--surrogate Wasserstein gap under an explicit compression assumption, whereas the noise-source analogue has a dimension-scale lower bound. We further characterize the conditional second moment of the direct surrogate-source training target and show that its source-dependent excess is small when the surrogate conditional law is close to the true conditional velocity law in mean and covariance. Empirically, on MNIST, CIFAR-10, ImageNet-32, and CelebA-HQ, the proposed method reaches competitive few-step generation under matched architectures.

Xiao Wang, Zihua She, Jianxi Su

Department of Statistics, Purdue University

Conditional Flow Matching Rectified Flow Flow-Based Generative Modeling Conditional Generative Modeling

May 12, 2026

Fast Image Super-Resolution via Consistency Rectified Flow

Diffusion models (DMs) have demonstrated remarkable success in real-world image super-resolution (SR), yet their reliance on time-consuming multi-step sampling largely hinders their practical applications. While recent efforts have introduced few- or single-step solutions, existing methods either inefficiently model the process from noisy input or fail to fully exploit iterative generative priors, compromising the fidelity and quality of the reconstructed images. To address this issue, we propose FlowSR, a novel approach that reformulates the SR problem as a rectified flow from low-resolution (LR) to high-resolution (HR) images. Our method leverages an improved consistency learning strategy to enable high-quality SR in a single step. Specifically, we refine the original consistency distillation process by incorporating HR regularization, ensuring that the learned SR flow not only enforces self-consistency but also converges precisely to the ground-truth HR target. Furthermore, we introduce a fast-slow scheduling strategy, where adjacent timesteps for consistency learning are sampled from two distinct schedulers: a fast scheduler with fewer timesteps to improve efficiency, and a slow scheduler with more timesteps to capture fine-grained texture details. Extensive experiments demonstrate that FlowSR achieves outstanding performance in both efficiency and image quality. Code: this https URL.

Jiaqi Xu, Wenbo Li, Haoze Sun +8

The Chinese University of Hong Kong · Huawei Noah’s Ark Lab · HKUST (GZ) +1

Rectified Flow Consistency Distillation Diffusion Model Acceleration Image Super-Resolution

May 10, 2026

Offline Preference Optimization for Rectified Flow with Noise-Tracked Pairs

Existing preference datasets for text-to-image models typically store only the final winner/loser images. This representation is insufficient for rectified flow (RF) models, whose generation is naturally indexed by a specific prior noise sample and follows a nearly straight denoising trajectory. In contrast, prior DPO-style alignment for diffusion models commonly estimates trajectories using an independent forward noising process, which can be mismatched to the true reverse dynamics and introduces unnecessary variance. We propose Prior Noise-Aware Preference Optimization (PNAPO), an off-policy alignment framework specialized for rectified flow. PNAPO augments preference data by retaining the paired prior noises used to generate each winner/loser image, turning the standard (prompt, winner, loser) triplet into a sextuple. Leveraging the straight-line property of RF, we estimate intermediate states via noise-image interpolation, which constrains the trajectory estimation space and yields a tighter surrogate objective for preference optimization. In addition, we introduce a dynamic regularization strategy that adapts the DPO regularization based on (i) the reward gap between winner and loser and (ii) training progress, improving stability and sample efficiency. Experiments on state-of-the-art RF T2I backbones show that PNAPO consistently improves preference metrics while substantially reducing training compute.

Yunhong Lu, Qichao Wang, Hengyuan Cao +2

Zhejiang University · Shanghai Institute for Advanced Study-Zhejiang University · Shanghai Institute for Mathematics and Interdisciplinary Sciences

T2I Generation Rectified Flow Text-Image Alignment Pairwise Preference Learning Flow-Based Generative Modeling Offline Preference Optimization+1

May 5, 2026

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics

Reconstructing PDE-governed fields from sparse and irregular measurements is challenging due to their ill-posed nature. Deterministic surrogates are trained on dense fields that struggle with limited measurements and uncertainty quantification. Generative models, by learning distributions over spatiotemporal fields, can better handle sparsity and uncertainty. However, existing generative approaches enforce data consistency and PDE constraints simultaneously via sampling-time gradient guidance, resulting in slow and unstable inference. To this end, we propose PerFlow, a Physics-embedded rectified Flow for efficient sparse reconstruction and uncertainty quantification of spatiotemporal dynamics. PerFlow decouples observation conditioning from physics enforcement, performing guidance-free conditioning by feeding observations into rectified-flow dynamics while embedding hard physics via a constraint-preserving projection (e.g., incompressibility or conservation). Theoretically, we establish invariance guarantees to ensure that trajectories remain on the physics-consistent manifold throughout sampling. Experiments on various PDE systems demonstrate competitive reconstruction accuracy with sound physics consistency, while enabling efficient conditional sampling (e.g., 50 steps) and up to 320x faster inference than 2000-step guided diffusion baselines.

Hao Zhou, Rui Zhang, Han Wan +1

Gaoling School of Artificial Intelligence, Renmin University of China

Physics-Informed Generative Modeling Uncertainty Quantification Rectified Flow Generative Modeling Physics-Informed ML Flow-Based Generative Modeling+1

Apr 21, 2026

IR-Flow: Bridging Discriminative and Generative Image Restoration via Rectified Flow

In image restoration, single-step discriminative mappings often lack fine details via expectation learning, whereas generative paradigms suffer from inefficient multi-step sampling and noise-residual coupling. To address this dilemma, we propose IR-Flow, a novel image restoration method based on Rectified Flow that serves as a unified framework bridging the gap between discriminative and generative paradigms. Specifically, we first construct multilevel data distribution flows, which expand the ability of models to learn from and adapt to various levels of degradation. Subsequently, cumulative velocity fields are proposed to learn transport trajectories across varying degradation levels, guiding intermediate states toward the clean target, while a multi-step consistency constraint is presented to enforce trajectory coherence and boost few-step restoration performance. We show that directly establishing a linear transport flow between degraded and clean image domains not only enables fast inference but also improves adaptability to out-of-distribution degradations. Extensive evaluations on deraining, denoising and raindrop removal tasks demonstrate that IR-Flow achieves competitive quantitative results with only a few sampling steps, offering an efficient and flexible framework that maintains an excellent distortion-perception balance. Our code is available at https://github.com/fanzh03/IR-Flow.

Zihao Fan, Xin Lu, Jie Xiao +3

MoE Key Laboratory of Brain-inspired Intelligent Perception and Cognition, School of Information Science and Technology, University of Science and Technology of China

Rectified Flow All-in-One Image Restoration Image Restoration Image Denoising

Apr 13, 2026

Precision Synthesis of Multi-Tracer PET via VLM-Modulated Rectified Flow for Stratifying Mild Cognitive Impairment

The biological definition of Alzheimer's disease (AD) relies on multi-modal neuroimaging, yet the clinical utility of positron emission tomography (PET) is limited by cost and radiation exposure, hindering early screening at preclinical or prodromal stages. While generative models offer a promising alternative by synthesizing PET from magnetic resonance imaging (MRI), achieving subject-specific precision remains a primary challenge. Here, we introduce DIReCT

++

, a Domain-Informed ReCTified flow model for synthesizing multi-tracer PET from MRI combined with fundamental clinical information. Our approach integrates a 3D rectified flow architecture to capture complex cross-modal and cross-tracer relationships with a domain-adapted vision-language model (BiomedCLIP) that provides text-guided, personalized generation using clinical scores and imaging knowledge. Extensive evaluations on multi-center datasets demonstrate that DIReCT

++

not only produces synthetic PET images (

^{18}

F-AV-45 and

^{18}

F-FDG) of superior fidelity and generalizability but also accurately recapitulates disease-specific patterns. Crucially, combining these synthesized PET images with MRI enables precise personalized stratification of mild cognitive impairment (MCI), advancing a scalable, data-efficient tool for the early diagnosis and prognostic prediction of AD. The source code will be released on https://github.com/ladderlab-xjtu/DIReCT-PLUS.

Tuo Liu, Shuijin Lin, Shaozhen Yan +4

School of Mathematics and Statistics, Xi’an Jiaotong University, No. 28, Xianning West Road, Xi’an, 710049, Shaanxi, China · Research Center for Intelligent Medical Equipment and Devices (IMED), Xi’an Jiaotong University, No. 28, Xianning West Road, Xi’an, 710049, Shaanxi, China · Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi’an Jiaotong University, No. 28, Xianning West Road, Xi’an, 710049, Shaanxi, China +1

Medical Image Synthesis Rectified Flow

Apr 10, 2026

MixFlow: Mixed Source Distributions Improve Rectified Flows

Diffusion models and their variations, such as rectified flows, generate diverse and high-quality images, but they are still hindered by slow iterative sampling caused by the highly curved generative paths they learn. An important cause of high curvature, as shown by previous work, is independence between the source distribution (standard Gaussian) and the data distribution. In this work, we tackle this limitation by two complementary contributions. First, we attempt to break away from the standard Gaussian assumption by introducing

κ\texttt{-FC}

, a general formulation that conditions the source distribution on an arbitrary signal

κ

that aligns it better with the data distribution. Then, we present MixFlow, a simple but effective training strategy that reduces the generative path curvatures and considerably improves sampling efficiency. MixFlow trains a flow model on linear mixtures of a fixed unconditional distribution and a

κ\texttt{-FC}

-based distribution. This simple mixture improves the alignment between the source and data, provides better generation quality with less required sampling steps, and accelerates the training convergence considerably. On average, our training procedure improves the generation quality by 12% in FID compared to standard rectified flow and 7% compared to previous baselines under a fixed sampling budget. Code available at: https://github.com/NazirNayal8/MixFlow

Nazir Nayal, Christopher Wewer, Jan Eric Lenssen

Max Planck Institute for Informatics, Saarland Informatics Campus, Germany

Rectified Flow Image Generation Flow-Based Generative Modeling Few-Step Diffusion Sampling

Apr 10, 2026

Truncated Rectified Flow Policy for Reinforcement Learning with One-Step Sampling

Maximum entropy reinforcement learning (MaxEnt RL) has become a standard framework for sequential decision making, yet its standard Gaussian policy parameterization is inherently unimodal, limiting its ability to model complex multimodal action distributions. This limitation has motivated increasing interest in generative policies based on diffusion and flow matching as more expressive alternatives. However, incorporating such policies into MaxEnt RL is challenging for two main reasons: the likelihood and entropy of continuous-time generative policies are generally intractable, and multi-step sampling introduces both long-horizon backpropagation instability and substantial inference latency. To address these challenges, we propose Truncated Rectified Flow Policy (TRFP), a framework built on a hybrid deterministic-stochastic architecture. This design makes entropy-regularized optimization tractable while supporting stable training and effective one-step sampling through gradient truncation and flow straightening. Empirical results on a toy multigoal environment and 10 MuJoCo benchmarks show that TRFP captures multimodal behavior effectively, outperforms strong baselines on most benchmarks under standard sampling, and remains highly competitive under one-step sampling.

Xubin Zhou, Yipeng Yang, Zhan Li

Harbin Institute of Technology

Maximum Entropy RL Continuous Control Rectified Flow RL for Generative Models

Apr 2, 2026

SteerFlow: Steering Rectified Flows for Faithful Inversion-Based Image Editing

Recent advances in flow-based generative models have enabled training-free, text-guided image editing by inverting an image into its latent noise and regenerating it under a new target conditional guidance. However, existing methods struggle to preserve source fidelity: higher-order solvers incur additional model inferences, truncated inversion constrains editability, and feature injection methods lack architectural transferability. To address these limitations, we propose SteerFlow, a model-agnostic editing framework with strong theoretical guarantees on source fidelity. In the forward process, we introduce an Amortized Fixed-Point Solver that implicitly straightens the forward trajectory by enforcing velocity consistency across consecutive timesteps, yielding a high-fidelity inverted latent. In the backward process, we introduce Trajectory Interpolation, which adaptively blends target-editing and source-reconstruction velocities to keep the editing trajectory anchored to the source. To further improve background preservation, we introduce an Adaptive Masking mechanism that spatially constrains the editing signal with concept-guided segmentation and source-target velocity differences. Extensive experiments on FLUX.1-dev and Stable Diffusion 3.5 Medium demonstrate that SteerFlow consistently achieves better editing quality than existing methods. Finally, we show that SteerFlow extends naturally to a complex multi-turn editing paradigm without accumulating drift.

Thinh Dao, Zhen Wang, Kien T. Pham +1

The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong · VinUniversity, Ha Noi, Viet Nam

Text-Guided Image Editing Flow-Based Generative Modeling Rectified Flow

Mar 30, 2026

ORSIFlow: Saliency-Guided Rectified Flow for Optical Remote Sensing Salient Object Detection

Optical Remote Sensing Image Salient Object Detection (ORSI-SOD) remains challenging due to complex backgrounds, low contrast, irregular object shapes, and large variations in object scale. Existing discriminative methods directly regress saliency maps, while recent diffusion-based generative approaches suffer from stochastic sampling and high computational cost. In this paper, we propose ORSIFlow, a saliency-guided rectified flow framework that reformulates ORSI-SOD as a deterministic latent flow generation problem. ORSIFlow performs saliency mask generation in a compact latent space constructed by a frozen variational autoencoder, enabling efficient inference with only a few steps. To enhance saliency awareness, we design a Salient Feature Discriminator for global semantic discrimination and a Salient Feature Calibrator for precise boundary refinement. Extensive experiments on multiple public benchmarks show that ORSIFlow achieves state-of-the-art performance with significantly improved efficiency.

Haojing Chen, Zhihang Liu, Yutong Li +3

University of Electronic Science and Technology of China, Chengdu, China · Hainan University, Haikou, China · China University of Mining & Technology (Beijing), Beijing, China

Salient Object Detection Rectified Flow

Mar 23, 2026

From Diffusion to Flow: Efficient Motion Generation in MotionGPT3

Recent text-driven motion generation methods span both discrete token-based approaches and continuous-latent formulations. MotionGPT3 exemplifies the latter paradigm, combining a learned continuous motion latent space with a diffusion-based prior for text-conditioned synthesis. While rectified flow objectives have recently demonstrated favorable convergence and inference-time properties relative to diffusion in image and audio generation, it remains unclear whether these advantages transfer cleanly to the motion generation setting. In this work, we conduct a controlled empirical study comparing diffusion and rectified flow objectives within the MotionGPT3 framework. By holding the model architecture, training protocol, and evaluation setup fixed, we isolate the effect of the generative objective on training dynamics, final performance, and inference efficiency. Experiments on the HumanML3D dataset show that rectified flow converges in fewer training epochs, reaches strong test performance earlier, and matches or exceeds diffusion-based motion quality under identical conditions. Moreover, flow-based priors exhibit stable behavior across a wide range of inference step counts and achieve competitive quality with fewer sampling steps, yielding improved efficiency-quality trade-offs. Overall, our results suggest that several known benefits of rectified flow objectives do extend to continuous-latent text-to-motion generation, highlighting the importance of the training objective choice in motion priors.

Jaymin Bhan, JiHong Jeon, SangYeop Jeong

Department of Applied Artificial Intelligence Seoul National University of Science and Technology

Text-to-Motion Generation Motion Diffusion Models Rectified Flow Flow-Based Generative Modeling

Mar 20, 2026

Improving Image-to-Image Translation via a Rectified Flow Reformulation

In this work, we propose Image-to-Image Rectified Flow Reformulation (I2I-RFR), a practical plug-in reformulation that recasts standard I2I regression networks as continuous-time transport models. While pixel-wise I2I regression is simple, stable, and easy to adapt across tasks, it often over-smooths ill-posed and multimodal targets, whereas generative alternatives often require additional components, task-specific tuning, and more complex training and inference pipelines. Our method augments the backbone input by channel-wise concatenation with a noise-corrupted version of the ground-truth target and optimizes a simple t-reweighted pixel loss. This objective admits a rectified-flow interpretation via an induced velocity field, enabling ODE-based progressive refinement at inference time while largely preserving the standard supervised training pipeline. In most cases, adopting I2I-RFR requires only expanding the input channels, and inference can be performed with a few explicit solver steps (e.g., 3 steps) without distillation. Extensive experiments across multiple image-to-image translation and video restoration tasks show that I2I-RFR generally improves performance across a wide range of tasks and backbones, with particularly clear gains in perceptual quality and detail preservation. Overall, I2I-RFR provides a lightweight way to incorporate continuous-time refinement into conventional I2I models without requiring a heavy generative pipeline.

Satoshi Iizuka, Shun Okamoto, Kazuhiro Fukui

University of Tsukuba

Image-to-Image Translation Rectified Flow Image Restoration Video Restoration

Mar 13, 2026

FLUX: Accelerating Cross-Embodiment Generative Navigation Policies via Rectified Flow and Static-to-Dynamic Learning

Autonomous navigation requires a broad spectrum of skills, from static goal-reaching to dynamic social traversal, yet evaluation remains fragmented across disparate protocols. We introduce DynBench, a dynamic navigation benchmark featuring physically valid crowd simulation. Combined with existing static protocols, it supports comprehensive evaluation across six fundamental navigation tasks. Within this framework, we propose FLUX, the first flow-based unified navigation policy. By linearizing probability flow, FLUX replaces iterative denoising with straight-line trajectories, improving per-step inference efficiency by 47% over prior flow-based methods and 29% over diffusion-based ones. Following a static-to-dynamic curriculum, FLUX initially establishes geometric priors and is subsequently refined through reinforcement learning in dynamic social environments. This regime not only strengthens socially-aware navigation but also enhances static task robustness by capturing recovery behaviors through stochastic action distributions. FLUX achieves state-of-the-art performance across all tasks and demonstrates zero-shot sim-to-real transfer on wheeled, quadrupedal, and humanoid platforms without any fine-tuning.

Zeying Gong, Yangyi Zhong, Yiyi Ding +6

The Hong Kong University of Science and Technology (Guangzhou) · The Hong Kong University of Science and Technology · National University of Singapore

Robot Navigation Benchmarks Robot Policy Learning Robot Navigation Cross-Embodiment Robot Learning Social Robot Navigation Rectified Flow

Mar 12, 2026

Generalization and Memorization in Rectified Flow

Generative models based on the Flow Matching objective, particularly Rectified Flow, have emerged as a dominant paradigm for efficient, high-fidelity image synthesis. However, while existing research heavily prioritizes generation quality and architectural scaling, the underlying dynamics of how RF models memorize training data remain largely underexplored. In this paper, we systematically investigate the memorization behaviors of RF through the test statistics of Membership Inference Attacks (MIA). We progressively formulate three test statistics, culminating in a complexity-calibrated metric that successfully decouples intrinsic image spatial complexity from genuine memorization signals. This calibration yields a significant performance surge -- boosting attack AUC by up to 15% and the privacy-critical TPR@1%FPR metric by up to 45% -- establishing the first non-trivial MIA specifically tailored for RF. Leveraging these refined metrics, we uncover a distinct temporal pattern: under standard uniform temporal training, a model's susceptibility to MIA strictly peaks at the integration midpoint, a phenomenon we justify via the network's forced deviation from linear approximations. Finally, we demonstrate that substituting uniform timestep sampling with a Symmetric Exponential (U-shaped) distribution effectively minimizes exposure to vulnerable intermediate timesteps. Extensive evaluations across three datasets confirm that this temporal regularization suppresses memorization while preserving generative fidelity.

Mingxing Rao, Daniel Moyer

Vanderbilt University, Nashville TN 37235, USA

Rectified Flow Membership Inference Attacks Memorization in Generative Models Generative Modeling Flow-Based Generative Modeling

Mar 5, 2026

Score-Guided Proximal Projection: A Unified Geometric Framework for Rectified Flow Editing

Rectified Flow (RF) models achieve state-of-the-art generation quality, yet controlling them for precise tasks -- such as semantic editing or blind image recovery -- remains a challenge. Current approaches bifurcate into inversion-based guidance, which suffers from "geometric locking" by rigidly adhering to the source trajectory, and posterior sampling approximations (e.g., DPS), which are computationally expensive and unstable. In this work, we propose Score-Guided Proximal Projection (SGPP), a unified framework that bridges the gap between deterministic optimization and stochastic sampling. We reformulate the recovery task as a proximal optimization problem, defining an energy landscape that balances fidelity to the input with realism from the pre-trained score field. We theoretically prove that this objective induces a normal contraction property, geometrically guaranteeing that out-of-distribution inputs are snapped onto the data manifold, and it effectively reaches the posterior mode constrained to the manifold. Crucially, we demonstrate that SGPP generalizes state-of-the-art editing methods: RF-inversion is effectively a limiting case of our framework. By relaxing the proximal variance, SGPP enables "soft guidance," offering a continuous, training-free trade-off between strict identity preservation and generative freedom.

Vansh Bansal, James G Scott

Department of Statistics and Data Sciences, UT Austin

Proximal Optimization Rectified Flow Score-Based Generative Modeling Image Restoration

Feb 28, 2026

RAFM: Retrieval-Augmented Flow Matching for Unpaired CBCT-to-CT Translation

Cone-beam CT (CBCT) is routinely acquired in radiotherapy but suffers from severe artifacts and unreliable Hounsfield Unit (HU) values, limiting its direct use for dose calculation. Synthetic CT (sCT) generation from CBCT is therefore an important task, yet paired CBCT--CT data are often unavailable or unreliable due to temporal gaps, anatomical variation, and registration errors. In this work, we introduce rectified flow (RF) into unpaired CBCT-to-CT translation in medical imaging. Although RF is theoretically compatible with unpaired learning through distribution-level coupling and deterministic transport, its practical effectiveness under small medical datasets and limited batch sizes remains underexplored. Direct application with random or batch-local pseudo pairing can produce unstable supervision due to semantically mismatched endpoint samples. To address this challenge, we propose Retrieval-Augmented Flow Matching (RAFM), which adapts RF to the medical setting by constructing retrieval-guided pseudo pairs using a frozen DINOv3 encoder and a global CT memory bank. This strategy improves empirical coupling quality and stabilizes unpaired flow-based training. Experiments on SynthRAD2023 under a strict subject-level true-unpaired protocol show that RAFM outperforms existing methods across FID, MAE, SSIM, PSNR, and SegScore. The code is available at https://github.com/HiLab-git/RAFM.git.

Xianhao Zhou, Jianghao Wu, Lanfeng Zhong +4

School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu, China · Faculty of Information Technology, Monash University, Melbourne, VIC 3800, Australia · Shanghai Artificial Intelligence Laboratory, Shanghai, China

Medical Image Synthesis Image-to-Image Translation Unpaired Image-to-Image Translation Flow Matching Cone-Beam CT Rectified Flow

Feb 22, 2026

CaReFlow: Cyclic Adaptive Rectified Flow for Multimodal Fusion

Modality gap significantly restricts the effectiveness of multimodal fusion. Previous methods often use techniques such as diffusion models and adversarial learning to reduce the modality gap, but they typically focus on one-to-one alignment without exposing the data points of the source modality to the global distribution information of the target modality. To this end, leveraging the characteristic of rectified flow that can map one distribution to another via a straight trajectory, we extend rectified flow for modality distribution mapping. Specifically, we leverage the

one-to-many mapping' strategy in rectified flow that allows each data point of the source modality to observe the overall target distribution. This also alleviates the issue of insufficient paired data within each sample, enabling a more robust distribution transformation. Moreover, to achieve more accurate distribution mapping and address the ambiguous flow directions in one-to-many mapping, we design

adaptive relaxed alignment', enforcing stricter alignment for modality pairs belonging to the same sample, while applying relaxed mapping for pairs not belonging to the same sample or category. Additionally, to prevent information loss during distribution mapping, we introduce `cyclic rectified flow' to ensure the transferred features can be translated back to the original features, allowing multimodal representations to learn sufficient modality-specific information. After distribution alignment, our approach achieves very competitive results on multiple tasks of multimodal affective computing even with a simple fusion method, and visualizations verify that it can effectively reduce the modality gap.

Sijie Mai, Shiqin Han

South China Normal University

Multimodal Fusion Cross-Modal Alignment Modality Gap in VLMs Rectified Flow Affective Computing

Jan 28, 2026

Order-Optimal Sample Complexity of Rectified Flows

Recently, flow-based generative models have shown superior efficiency compared to diffusion models. In this paper, we study rectified flow models, which constrain transport trajectories to be linear from the base distribution to the data distribution. This structural restriction greatly accelerates sampling, often enabling high-quality generation with a single Euler step. Under standard assumptions on the neural network classes used to parameterize the velocity field and data distribution, we prove that rectified flows achieve sample complexity

\tilde{O}(\varepsilon^{-2})

. This improves on the best known

O(\varepsilon^{-4})

bounds for flow matching model and matches the optimal rate for mean estimation. Our analysis exploits the particular structure of rectified flows: because the model is trained with a squared loss along linear paths, the associated hypothesis class admits a sharply controlled localized Rademacher complexity. This yields the improved, order-optimal sample complexity and provides a theoretical explanation for the strong empirical performance of rectified flow models.

Hari Krishna Sahoo, Mudit Gaur, Vaneet Aggarwal

Purdue University

Rectified Flow Flow-Based Generative Modeling Sample Complexity

Nov 11, 2025

SeFA-Policy: Fast and Accurate Visuomotor Policy Learning with Selective Flow Alignment

Developing efficient and accurate visuomotor policies poses a central challenge in robotic imitation learning. While recent rectified flow approaches have advanced visuomotor policy learning, they suffer from a key limitation: After iterative distillation, generated actions may deviate from the ground-truth actions corresponding to the current visual observation, leading to accumulated error as the reflow process repeats and unstable task execution. We present Selective Flow Alignment (SeFA), an efficient and accurate visuomotor policy learning framework. SeFA resolves this challenge by a selective flow alignment strategy, which leverages expert demonstrations to selectively correct generated actions and restore consistency with observations, while preserving multimodality. This design introduces a consistency correction mechanism that ensures generated actions remain observation-aligned without sacrificing the efficiency of one-step flow inference. Extensive experiments across both simulated and real-world manipulation tasks show that SeFA Policy surpasses state-of-the-art diffusion-based and flow-based policies, achieving superior accuracy and robustness while reducing inference latency by over 98%. By unifying rectified flow efficiency with observation-consistent action generation, SeFA provides a scalable and dependable solution for real-time visuomotor policy learning. Code is available on https://github.com/RongXueZoe/SeFA.

Rong Xue, Jiageng Mao, Mingtong Zhang +1

University of Southern California

Rectified Flow Visuomotor Policy Learning Robotic Manipulation Robot Imitation Learning

Sep 27, 2025

RestoRect: Degraded Image Restoration via Latent Rectified Flow & Feature Distillation

Current approaches for restoration of degraded images face a trade-off: high-performance models are slow for practical use, while fast models produce poor results. Knowledge distillation transfers teacher knowledge to students, but existing static feature matching methods cannot capture how modern transformer architectures dynamically generate features. We propose a novel Latent Rectified Flow Feature Distillation method for restoring degraded images called 'RestoRect'. We apply rectified flow to reformulate feature distillation as a generative process where students learn to synthesize teacher-quality features through learnable trajectories in latent space. Our framework combines Retinex decomposition with learnable anisotropic diffusion constraints, and trigonometric color space polarization. We introduce a Feature Layer Extraction loss for robust knowledge transfer between different network architectures through cross-normalized transformer feature alignment with percentile-based outlier detection. RestoRect achieves better training stability, and faster convergence and inference while preserving restoration quality, demonstrating superior results across 15 image restoration datasets, covering 4 tasks, on 10 metrics against baselines.

Shourya Verma, Mengbo Wang, Nadia Atallah Lanman +1

Department of Computer Science, Purdue University, USA · Purdue Institute of Cancer Research, USA

Image Restoration Feature-Based Knowledge Distillation Degradation-Aware Image Restoration Rectified Flow