这篇论文用严格理论证明和实验验证了整流流中自蒸馏的改进方法，想了解生成模型自训练优化的可以看看。
该论文研究了整流流（Rectified Flow）的最优自蒸馏问题，其中学生模型在真实RF速度和教师速度的混合数据上训练，理论证明可提升教师模型。对于带有岭正则化的线性RF，作者推导了精确的仿射路径恒等式，并给出了最优混合系数的闭式解，正混合修正欠正则化教师，负混合修正过正则化教师。同时提出了一次广义交叉验证（GCV）方法，避免网格搜索和重复重拟合。实验在高斯模型、高斯混合和图像数据上验证，该方法在速度风险、模态恢复和有限步生成上均优于教师和纯蒸馏。
Optimal Self-Distillation for Rectified Flow via Linear Probing
Modern generative models are increasingly trained using model-generated signals, creating both opportunities for self-improvement and risks of collapse. We study optimal self-distillation (SD) for rectified flow (RF): given a suboptimal teacher velocity field, can a student trained on a mixture of true RF velocities and teacher velocities provably improve the teacher? For linear RF with ridge regularization on fixed interpolation pairs, we prove an exact affine path identity, derive the optimal mixing coefficient in closed form, and show strict improvement in integrated velocity risk whenever the teacher risk is nonstationary along the regularization path. The optimal coefficient obeys a sign rule: positive mixing corrects under-regularized teachers, while negative mixing corrects over-regularized teachers. We also give one-shot generalized cross-validation (GCV) and validation tuning procedure that avoids grid search over mixing weights and repeated refitting. Combining this theorem with RF Wasserstein convergence bounds, we show that optimal self-distillation improves the velocity estimation terms controlling continuous-time and finite-step generation error. Experiments with Gaussian models, Gaussian mixtures, and image data show that optimal self-distillation improves velocity risk, mode recovery, and finite-step generation relative to both the teacher and pure distillation.