Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow

By Xingchao Liu, Chengyue Gong, Qiang Liu. 2022

3,494 citations recorded by the source corpus.

We present rectified flow, a surprisingly simple approach to learning (neural) ordinary differential equation (ODE) models to transport between two empirically observed distributions \pi_0 and \pi_1, hence providing a unified solution to generative modeling and domain transfer, among various other tasks involving distribution transport. The idea of rectified flow is to learn the ODE to follow the straight paths connecting the points drawn from \pi_0 and \pi_1 as much as possible. This is achieved by solving a straightforward nonlinear least squares optimization problem, which can be easily scaled to large models without introducing extra parameters beyond standard supervised learning. The straight paths are special and preferred because they are the shortest paths between two points, and can be simulated exactly without time discretization and hence yield computationally efficient models. We show that the procedure of learning a rectified flow from data, called rectification, turns an arbitrary coupling of \pi_0 and \pi_1 to a new deterministic coupling with provably non-increasing convex transport costs. In addition, recursively applying rectification allows us to obtain a sequence of flows with increasingly straight paths, which can be simulated accurately with coarse time discretization in the inference phase. In empirical studies, we show that rectified flow performs superbly on image generation, image-to-image translation, and domain adaptation. In particular, on image generation and translation, our method yields nearly straight flows that give high quality results even with a single Euler discretization step.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Computer Vision and Pattern Recognition

In Statistical and Nonlinear Physics

Citations in the corpus

Flow Matching for Generative Modeling (2022, neutral): “Lastly, concurrently to our work (Liu et al., 2022; Albergo & Vanden-Eijnden, 2022) arrived at similar conditional objectives for simulation-free training of CNFs, while Neklyudov et al.”
Stochastic Interpolants: A Unifying Framework for Flows and Diffusions (2023, methodology): “• Our approach is amenable to a bias-free variant of the rectification procedure proposed in [30], as discussed in Section 3.”
Building Normalizing Flows with Stochastic Interpolants (2022, neutral): “Co-incident works by Liu et al. (2022); Lipman et al. (2022) derive an analogous optimization to us, with a focus on straight interpolants, also contrasting it with score-based methods.”
FLUX.1 Kontext: Flow Matching for In-Context Image Generation and Editing in Latent Space (2025, neutral): “2 FLUX.1 FLUX.1 is a rectified flow transformer [12, 30, 32] trained in the latent space of an image autoen-coder [42].”
InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation (2023, methodology): “Fortunately, it was observed in [1] that the trajectories of ODE [ v k ] becomes nearly (even though not exactly) straight with even one or two steps of reflows.”
DanceGRPO: Unleashing GRPO on Visual Generation (2025, neutral): “Rectified Flow [6] .”
SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers (2024, methodology): “Velocity field parameterizations using the Linear interpolant were also studied in [39, 42], and were generalized to the manifold setting in [6].”
Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think (2024, neutral): “Different from DDPM, flow matching models (Esser et al., 2024; Lipman et al., 2022; Liu et al., 2023) deal with the continuous time-dependent process with a data x ∗ ∼ p ( x ) and a Gaussian noise ϵ ∼ N ( 0 , I ) on t ∈ [0 , 1] : where α t and σ t are a decreasing and increasing function of t…”
Mean Flows for One-step Generative Modeling (2025, neutral): “Flow Matching [28, 1, 30] provides an intuitive and conceptually simple framework for constructing flow paths that transport one distribution to another.”
Qwen-Image Technical Report (2025, positive): “According to Rectified Flow (Liu et al., 2022; Esser et al., 2024), the intermediate latent variable at timestep t and its corresponding velocity v t can be calculated as: Then, the model is trained to predict the target velocity, and the loss function is defined as the mean squared error (MSE) betw”
DiffusionDrive: Truncated Diffusion Model for End-to-End Autonomous Driving (2024, neutral): “Flow matching [30, 31] further optimizes the generative process by directly modeling continuous probability ﬂows.”
Retrieval-Augmented Generation for AI-Generated Content: A Survey (2024, neutral): “In this section, we introduce RAG foundations and outline enhancement methods that further improve the effectiveness.”
Hunyuan3D 2.0: Scaling Diffusion Models for High Resolution Textured 3D Assets Generation (2025, positive): “The success of diffusion models [33] and their variants [58, 53] in text-conditioned image [74, 45] generation has spurred the popularity of diffusion-based shape generative models, with notable works [16, 119] achieving stable cross-category shape generation.”
From Slow Bidirectional to Fast Autoregressive Video Diffusion Models (2024, positive): “Rectified flow [14, 46, 47] trains a student model on the linear interpolation path of noise-image pairs obtained from the teacher.”
EDICT: Exact Diffusion Inversion via Coupled Transformations (2022, neutral): “Multi-step or higher-order methods that parallel DDIM have also been proposed [17, 19], including methods that aim to reducing the computational time for generation [13, 18].”
Adversarial Diffusion Distillation (2023, methodology): “InstaFlow [36] propose to use Rectiﬁed Flows [35] to facilitate a better distillation process.”