Related papers: Statistical Properties of Rectified Flow
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…
The unsupervised task of aligning two or more distributions in a shared latent space has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. Existing flow-based approaches estimate…
The fundamental relationship of traffic flow is empirically estimated by fitting a regression curve to a cloud of observations of traffic variables. Such estimates, however, may suffer from the confounding/endogeneity bias due to omitted…
As an example for the optimization of unstable flows, we present an economics-based method for deciding the optimal rates at which vehicles are allowed to enter a highway. It exploits the naturally occuring fluctuations of traffic flow and…
Models involving branched structures are employed to describe several supply-demand systems such as the structure of the nerves of a leaf, the system of roots of a tree and the nervous or cardiovascular systems. Given a flow (traffic path)…
Quantifying differences between flow fields is a key challenge in fluid mechanics, particularly when evaluating the effectiveness of flow control. Traditional vector metrics, such as the Euclidean distance, provide straightforward pointwise…
Modern technologies are generating ever-increasing amounts of data. Making use of these data requires methods that are both statistically sound and computationally efficient. Typically, the statistical and computational aspects are treated…
Motivated by the need for accurate traffic flow prediction in transportation management, we propose a functional data method to analyze traffic flow patterns and predict future traffic flow. In this study we approach the problem by sampling…
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…
We propose two new evaluation metrics to assess realness of generated images based on normalizing flows: a simpler and efficient flow-based likelihood distance (FLD) and a more exact dual-flow based likelihood distance (D-FLD). Because…
Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…
Score-based or diffusion models generate high-quality tabular data, surpassing GAN-based and VAE-based models. However, these methods require substantial training time. In this paper, we introduce RecTable, which uses the rectified flow…
In this paper we analyze the transport of passive tracers by deterministic stationary incompressible flows which can be decomposed over an infinite number of spatial scales without separation between them. It appears that a low order…
The fundamental diagram (FD), also known as the flow--density relation, is one of the most fundamental concepts in the traffic flow theory. It describes the relation between equilibrated flow, density, and speed in traffic flow.…
We study Variational Rectified Flow Matching, a framework that enhances classic rectified flow matching by modeling multi-modal velocity vector-fields. At inference time, classic rectified flow matching 'moves' samples from a source…
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…
Uncertainty often plays an important role in dynamic flow problems. In this paper, we consider both, a stationary and a dynamic flow model with uncertain boundary data on networks. We introduce two different ways how to compute the…
In its simplest form, the traffic flow prediction problem is restricted to predicting a single time-step into the future. Multi-step traffic flow prediction extends this set-up to the case where predicting multiple time-steps into the…
Experimental studies on vehicular traffic provide data on quantities like density, flux, and mean speed of the vehicles. However, the diagrams relating these variables (the fundamental and speed diagrams) show some peculiarities not yet…
Recent studies on transportation networks have shown that real-time route guidance can inadvertently induce congestion or oscillatory traffic patterns. Nevertheless, such technologies also offer a promising opportunity to manage traffic…