A Flow Matching Algorithm for Many-Shot Adaptation to Unseen Distributions

2026-05-07

AI Summary

This work investigates how generative models can efficiently adapt to generate data from unseen distributions given only a few examples. To this end, the authors propose Functional Projection Flow Matching (FP-FM), which uniquely integrates basis function expansions with flow matching: during training, basis functions of the velocity field for the source distribution are learned, and at inference time, adaptation to a new target distribution is achieved by least-squares projection onto these bases—requiring no additional training. The method incorporates variants such as time-dependent coefficients to balance representational capacity and computational cost. Experiments demonstrate that FP-FM significantly outperforms existing baselines on both synthetic and image data, achieving notably higher generation precision and recall on unseen distributions.

Abstract

While generative modeling has achieved remarkable success on tasks like natural language-conditioned image generation, enabling model adaptation from example data points remains a relatively underexplored and challenging problem. To this end, we propose Function Projection for Flow Matching (FP-FM), an algorithm that directly conditions generation on samples from the target distribution. FP-FM learns basis functions to span the velocity fields corresponding to a set of training distributions, and adapts to new distributions by computing a simple least-squares projection onto this basis. This enables efficient generation of samples from diverse target distributions without additional training at inference time. We further introduce multiple variants of FP-FM that provide a trade-off in expressivity and compute by enriching the coefficient calculation, e.g., by making the coefficients dependent on time. FP-FM achieves greatly improved precision and recall relative to baselines across synthetic and image-based datasets, with especially strong gains on unseen distributions.

Problem

• generative modeling
• distribution adaptation
• unseen distributions
• example-based adaptation
• flow matching

Innovation

• Flow Matching
• Function Projection
• Many-Shot Adaptation
• Unseen Distribution Generalization
• Velocity Field Basis