Related papers: Order-Optimal Sample Complexity of Rectified Flows

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…

Transport maps can ease the sampling of distributions with non-trivial geometries by transforming them into distributions that are easier to handle. The potential of this approach has risen with the development of Normalizing Flows (NF)…

Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods have been focused on the static formulation of the OT…

Flow matching models generate samples by numerically integrating a learned velocity field, with each integration step requiring a neural network evaluation. Fast generation therefore requires using a small fixed evaluation budget…

Fast flow models accelerate the iterative sampling process by learning to directly predict ODE path integrals, enabling one-step or few-step generation. However, we argue that current fast-flow training paradigms suffer from two fundamental…

The performance of flow matching and diffusion models can be greatly improved at inference time using reward alignment algorithms, yet efficiency remains a major limitation. While several algorithms were proposed, we demonstrate that a…

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…

In this work, we propose a new family of generative flows on an augmented data space, with an aim to improve expressivity without drastically increasing the computational cost of sampling and evaluation of a lower bound on the likelihood.…

Normalizing flows are a popular class of models for approximating probability distributions. However, their invertible nature limits their ability to model target distributions whose support have a complex topological structure, such as…

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…

Flow Matching has limited ability in achieving one-step generation due to its reliance on learned curved trajectories. Previous studies have attempted to address this limitation by either modifying the coupling distribution to prevent…

Dataset distillation compresses large datasets into compact synthetic sets with comparable performance in training models. Despite recent progress on diffusion-based distillation, this type of method typically depends on heuristic guidance…

Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable…

One-step generative modeling has emerged as a leading approach to amortize the inference cost of diffusion and flow-matching models. Among distillation-free methods, MeanFlow training is notoriously unstable, with non-decreasing loss and…

Diffusion Probabilistic Models (DPMs) have demonstrated exceptional capability of generating high-quality and diverse images, but their practical application is hindered by the intensive computational cost during inference. The DPM…

Generative modeling techniques such as Diffusion and Flow Matching have achieved significant successes in generating designable and diverse protein backbones. However, many current models are computationally expensive, requiring hundreds or…

A generative model based on a continuous-time normalizing flow between any pair of base and target probability densities is proposed. The velocity field of this flow is inferred from the probability current of a time-dependent density that…

Reduced order models play an important role in the design, optimization and control of dynamical systems. In recent years, there has been an increasing interest in the application of data-driven techniques for model reduction that can…

Score-based generative models have emerged as a powerful approach for sampling high-dimensional probability distributions. Despite their effectiveness, their theoretical underpinnings remain relatively underdeveloped. In this work, we study…

Flow-based generative models have demonstrated promising performance across a broad spectrum of data modalities (e.g., image and text). However, there are few works exploring their extension to unordered data (e.g., spatial point set),…