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Rectified flow is a generative model that learns smooth transport mappings between two distributions through an ordinary differential equation (ODE). Unlike diffusion-based generative models, which require costly numerical integration of a…
Diffusion models have greatly improved visual generation but are hindered by slow generation speed due to the computationally intensive nature of solving generative ODEs. Rectified flow, a widely recognized solution, improves generation…
We present a flow-based approach to the optimal transport (OT) problem between two continuous distributions $\pi_0,\pi_1$ on $\mathbb{R}^d$, of minimizing a transport cost $\mathbb{E}[c(X_1-X_0)]$ in the set of couplings $(X_0,X_1)$ whose…
This paper investigates the connections between rectified flows, flow matching, and optimal transport. Flow matching is a recent approach to learning generative models by estimating velocity fields that guide transformations from a source…
We formulate a hierarchical rectified flow to model data distributions. It hierarchically couples multiple ordinary differential equations (ODEs) and defines a time-differentiable stochastic process that generates a data distribution from a…
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…
Diffusion models have shown great promise for image and video generation, but sampling from state-of-the-art models requires expensive numerical integration of a generative ODE. One approach for tackling this problem is rectified flows,…
Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, although theoretical results supporting the validity of these…
Recently, the rectified flow (RF) has emerged as the new state-of-the-art among flow-based diffusion models due to its high efficiency advantage in straight path sampling, especially with the amazing images generated by a series of RF…
Semantic segmentation and semantic image synthesis are two representative tasks in visual perception and generation. While existing methods consider them as two distinct tasks, we propose a unified framework (SemFlow) and model them as a…
Pre-trained diffusion models are commonly used to generate clean data (e.g., images) from random noises, effectively forming pairs of noises and corresponding clean images. Distillation on these pre-trained models can be viewed as the…
Recent works on optical flow estimation use neural networks to predict the flow field that maps positions of one image to positions of the other. These networks consist of a feature extractor, a correlation volume, and finally several…
Deterministic flow models, such as rectified flows, offer a general framework for learning a deterministic transport map between two distributions, realized as the vector field for an ordinary differential equation (ODE). However, they are…
Diffusion models create data from noise by inverting the forward paths of data towards noise and have emerged as a powerful generative modeling technique for high-dimensional, perceptual data such as images and videos. Rectified flow is a…
Flow matching has emerged as a simulation-free alternative to diffusion-based generative modeling, producing samples by solving an ODE whose time-dependent velocity field is learned along an interpolation between a simple source…
Existing rectified flow models are based on linear trajectories between data and noise distributions. This linearity enforces zero curvature, which can inadvertently force the image generation process through low-probability regions of the…
Over the several recent years, there has been a boom in development of Flow Matching (FM) methods for generative modeling. One intriguing property pursued by the community is the ability to learn flows with straight trajectories which…
Ordinary differential equation (ODE) based generative models have emerged as a powerful approach for producing high-quality samples in many applications. However, the ODE-based methods either suffer the discretization error of numerical…
Enhancing the efficiency of high-quality image generation using Diffusion Models (DMs) is a significant challenge due to the iterative nature of the process. Flow Matching (FM) is emerging as a powerful generative modeling paradigm based on…
Diffusion models have significantly improved the quality and diversity of audio generation but are hindered by slow inference speed. Rectified flow enhances inference speed by learning straight-line ordinary differential equation (ODE)…