直接学习数据生成映射，实现单次前向传播完成采样。
ODE-free Neural Flow Matching for One-Step Generative Modeling
- 用神经流直接建模从噪声到数据的映射关系，无需积分路径。
- 在MNIST和CIFAR-10上达到与扩散模型相当的生成质量。
- 通过最优传输配对防止均值坍塌，适合追求高效推理的场景。
扩散模型与流匹配通过学习随时间变化的向量场，将噪声逐步转换为数据，推理时需数十至数百次网络评估。本文提出无微分方程的生成框架——最优传输神经流匹配（OT-NFM），直接以神经流参数化传输映射，实现真正的一步生成，仅需一次前向传播。我们发现，朴素的流映射训练会导致均值坍塌，即噪声-数据配对不一致使所有输出趋近数据均值。理论证明一致耦合对非退化学习至关重要，并引入可扩展的小批量与在线耦合策略解决该问题。在合成基准及图像生成任务（MNIST、CIFAR-10）上的实验表明，该方法在保持竞争性样本质量的同时，将推理次数缩减为单次网络评估。
原文摘要 · Abstract (English)
Diffusion and flow matching models generate samples by learning time-dependent vector fields whose integration transports noise to data, requiring tens to hundreds of network evaluations at inference. We instead learn the transport map directly. We propose Optimal Transport Neural Flow Matching (OT-NFM), an ODE-free generative framework that parameterizes the flow map with neural flows, enabling true one-step generation with a single forward pass. We show that naive flow-map training suffers from mean collapse, where inconsistent noise-data pairings drive all outputs toward the data mean. We prove that consistent coupling is necessary for non-degenerate learning and address this using optimal transport pairings with scalable minibatch and online coupling strategies. Experiments on synthetic benchmarks and image generation tasks (MNIST and CIFAR-10) demonstrate competitive sample quality while reducing inference to a single network evaluation.
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