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Flow Matching, a promising approach in generative modeling, has recently gained popularity. Relying on ordinary differential equations, it offers a simple and flexible alternative to diffusion models, which are currently the…
Score-based generative models are a popular class of generative modelling techniques relying on stochastic differential equations (SDE). From their inception, it was realized that it was also possible to perform generation using ordinary…
Generative modelling has seen significant advances through simulation-free paradigms such as Flow Matching, and in particular, the MeanFlow framework, which replaces instantaneous velocity fields with average velocities to enable efficient…
Flow matching has recently emerged as a promising alternative to diffusion-based generative models, offering faster sampling and simpler training by learning continuous flows governed by ordinary differential equations. Despite growing…
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…
Forecasting high-dimensional, PDE-governed dynamics remains a core challenge for generative modeling. Existing autoregressive and diffusion-based approaches often suffer cumulative errors and discretisation artifacts that limit long,…
Score-based generative models have excellent performance in terms of generation quality and likelihood. They model the data distribution by matching a parameterized score network with first-order data score functions. The score network can…
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 present theoretical convergence guarantees for ODE-based generative models, specifically flow matching. We use a pre-trained autoencoder network to map high-dimensional original inputs to a low-dimensional latent space, where a…
Diffusion models have exhibited excellent performance in various domains. The probability flow ordinary differential equation (ODE) of diffusion models (i.e., diffusion ODEs) is a particular case of continuous normalizing flows (CNFs),…
Prior flow matching methods in robotics have primarily learned velocity fields to morph one distribution of trajectories into another. In this work, we extend flow matching to capture second-order trajectory dynamics, incorporating…
Flow Matching (FM) models achieve remarkable results in generative tasks. Building upon diffusion models, FM's simulation-free training paradigm enables simplicity and efficiency but introduces a train-inference gap: model outputs cannot be…
We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for…
Elucidating reaction mechanisms hinges on efficiently generating transition states (TSs), products, and complete reaction networks. Recent generative models, such as diffusion models for TS sampling and sequence-based architectures for…
Autoregressive generative PDE solvers can be accurate one step ahead yet drift over long rollouts, especially in coarse-to-fine regimes where each step must regenerate unresolved fine scales. This is the regime of diffusion and…
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…
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…
Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different…
Flow matching (FM) is increasingly used in scientific domains for time series generation and forecasting, where data often arise from underlying dynamical systems. However, it is not well-understood whether it learns transferable dynamical…
Deep generative models aim to learn the underlying distribution of data and generate new ones. Despite the diversity of generative models and their high-quality generation performance in practice, most of them lack rigorous theoretical…