提出SGFlow，高效学习扩散模型的流映射，兼顾速度与理论保证。
Flow Map Learning via Nongradient Vector Flow
- 基于非保守动力学直接学习流映射，无需模型逆或迭代梯度。
- 在CIFAR上10步采样时FID最优，其他步数也保持竞争力。
- 唯一证明停止梯度动力学有稳定点的流映射方法，适合追求理论可靠性的研究者。
扩散模型和流模型得益于简单的回归损失，但推理开销大，因采样需积分。一致性模型通过直接学习沿常微分方程（ODE）轨迹的流映射，开辟了单步与多步之间的新设计空间。然而，现有方法存在计算挑战：需模型逆或反向传播通过迭代模型调用，且未证明所求的ODE流映射是损失函数的解。本文提出SGFlow，一种学习流映射的方法，绕过显式可逆性约束和昂贵的模型迭代梯度计算。SGFlow通过遵循在目标流映射处具有不动点的非保守动力学，从零开始训练模型以同时计算ODE解和隐含速度。在CIFAR图像基准上，没有单一方法在所有步数下均取得最佳FID：SGFlow在10步采样时达到最优FID，且在其他步数下与流匹配、均值流和拉格朗日映射匹配方法表现相当；同时，它是唯一一个对基于停止梯度的动力学提供不动点保证的方法。
原文摘要 · Abstract (English)
Diffusion and flow-based models benefit from simple regression losses, but inference incurs significant overhead because sampling requires integration. Consistency models address this by directly learning the flow maps along the ODE trajectory, opening a design space between one-step and many-step approaches. However, existing methods face computational challenges such as requiring model inverses or backpropagation through iterated model calls, and do not always prove that the desired ODE flow map is a solution to the loss. We introduce SGFlow, an approach for learning flow maps that bypasses explicit invertibility constraints and expensive differentiation through model iteration. SGFlow trains a model to compute both the ODE solutions and the implied velocity from scratch by following non-conservative dynamics with a stationary point at the desired flow map. On the CIFAR image benchmark, no single method attains the best FID at every step count: SGFlow attains the best FID at 10 sampling steps and remains competitive with flow matching, Meanflow, and Lagrangian map matching at other step counts, while being the only one with a proven stationary-point guarantee for its stopgrad-based dynamics.
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