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Joint CFM objective

The Joint Conditional Flow Matching objective is a simulation-free training loss function for continuous-time generative models that trains a neural network to approximate a marginal vector field using conditional vector fields defined over paired source and target distributions. Unlike standard conditional flow matching methods that rely on independently drawn noise and data samples, the joint objective incorporates a general joint distribution or coupling over the endpoints while preserving the target marginal constraints. By minimizing the expected squared error between the parameterized vector field and the conditional velocity trajectories over time, this objective reduces gradient variance during optimization and produces straighter probability paths, allowing continuous normalizing flows to generate high-quality samples with fewer numerical integration steps.

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Multisample Flow Matching: Straightening Flows with Minibatch Couplings

Aram-Alexandre Pooladian, Heli Ben-Hamu, Carles Domingo-Enrich, Brandon Amos, Yaron Lipman, Ricky T. Q. Chen

OrganizationsMetaNew York UniversityWeizmann Institute of Science

Why you should read this

Proposes Multisample Flow Matching, a simulation-free training framework that couples minibatch data and noise distributions to straighten probability paths, reducing gradient variance during training and enabling faster generative sampling with fewer model evaluations.

Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples. Recent works, such as Flow Matching, derived paths that are optimal for each data sample. However, these algorithms rely on independent data and noise samples, and do not exploit underlying structure in the data distribution for constructing probability paths. We propose Multisample Flow Matching, a more general framework that uses non-trivial couplings between data and noise samples while satisfying the correct marginal constraints. At very small overhead costs, this generalization allows us to (i) reduce gradient variance during training, (ii) obtain straighter flows for the learned vector field, which allows us to generate high-quality samples using fewer function evaluations, and (iii) obtain transport maps with lower cost in high dimensions, which has applications beyond generative modeling. Importantly, we do so in a completely simulation-free manner with a simple minimization objective. We show that our proposed methods improve sample consistency on downsampled ImageNet data sets, and lead to better low-cost sample generation.

Source

https://arxiv.org/pdf/2304.14772

Added

2026-09-28