New Quantile Coupling Improves Flow Matching for Generative Models

Flow Matching is a technique used to train generative models by learning the velocity field of a probability path between a simple source distribution and a complex target data distribution. The way source and target samples are paired, known as coupling, significantly impacts the model's performance. Traditional structured couplings often involve computationally expensive mini-batch transport or assignment procedures. A new method, Quantile Coupling Flow Matching (QC-FM), proposes a more efficient one-sided coupling. Instead of matching two pre-sampled batches, QC-FM samples only the data batch and directly constructs each corresponding source sample. It achieves this by mapping data ranks along random orthogonal directions to Gaussian quantiles and completing the latent code with conditional Gaussian sampling. This approach eliminates irreducible regression variance along selected slices, making the ideal flow straighter without altering the sampling prior. Experiments across various datasets like CIFAR-10 and CelebA show that QC-FM significantly improves over baseline methods, reducing FID scores by up to 12.9% and outperforming other advanced techniques.