Related papers: Flow Matching on Lie Groups

This paper introduces Gauge Flow Models, a novel class of Generative Flow Models. These models incorporate a learnable Gauge Field within the Flow Ordinary Differential Equation (ODE). A comprehensive mathematical framework for these…

Learning-based optical flow estimation has been dominated with the pipeline of cost volume with convolutions for flow regression, which is inherently limited to local correlations and thus is hard to address the long-standing challenge of…

Diffusion models approximate the denoising distribution as a Gaussian and predict its mean, whereas flow matching models reparameterize the Gaussian mean as flow velocity. However, they underperform in few-step sampling due to…

We propose a principled and effective framework for one-step generative modeling. We introduce the notion of average velocity to characterize flow fields, in contrast to instantaneous velocity modeled by Flow Matching methods. A…

Flow Matching has become a cornerstone of modern generative models like Stable Diffusion 3, largely due to the efficiency of its Rectified Flow (RF) variant. The success of RF hinges on iteratively learning straight trajectories, pushing…

Over the past decade, advances in generative modeling, such as generative adversarial networks, masked autoencoders, and diffusion models, have significantly transformed biological research and discovery, enabling breakthroughs in molecule…

Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation…

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…

Flow matching has emerged as a powerful generative framework, with recent few-step methods achieving remarkable inference acceleration. However, we identify a critical yet overlooked limitation: these models suffer from severe diversity…

Flow matching has recently emerged as a promising alternative to diffusion-based generative models, particularly for text-to-image generation. Despite its flexibility in allowing arbitrary source distributions, most existing approaches rely…

High-dimensional integration with respect to complex target measures remains a fundamental challenge in computational science. While Flow Matching (FM) offers a powerful paradigm for constructing continuous-time transport maps, its…

Controlling generative models is computationally expensive. This is because optimal alignment with a reward function--whether via inference-time steering or fine-tuning--requires estimating the value function. This task demands access to…

Accurate emulation of multi-scale physical systems governed by PDEs demands models that remain stable over long autoregressive rollouts while preserving fine-scale structures. Deterministic emulators produce overly-smoothed predictions,…

Reinforcement learning has emerged as a promising paradigm for aligning diffusion and flow-matching models with human preferences, yet practitioners face fragmented codebases, model-specific implementations, and engineering complexity. We…

Sequential probabilistic inference from streaming observations requires modeling distributions over future trajectories as new observations arrive. Although diffusion and flow-matching models are effective at capturing high-dimensional,…

In this paper, we present a comprehensive theoretical comparison of diffusion and flow matching under the Generator Matching framework. Despite their apparent differences, both diffusion and flow matching can be viewed under the unified…

Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative…

Taming the generation outcome of state of the art Diffusion and Flow-Matching (FM) models without having to re-train a task-specific model unlocks a powerful tool for solving inverse problems, conditional generation, and controlled…

Current auto-regressive (AR) LLMs, diffusion-based text/image generative models, and recent flow matching (FM) algorithms are capable of generating premium quality text/image samples. However, the inference or sample generation in these…

Visually-guided acoustic highlighting seeks to rebalance audio in alignment with the accompanying video, creating a coherent audio-visual experience. While visual saliency and enhancement have been widely studied, acoustic highlighting…