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Variance Reduction for Expectations with Diffusion Teachers Decision-Path Patterns as Tree Reliability Signals: Path-based Adaptive Weighting for Random Forest Classification The General Theory of Localization Methods CASCADE Conformal Prediction: Uncertainty-Adaptive Prediction Intervals for Two-Stage Clinical Decision Support Symmetrization of Loss Functions for Robust Training of Neural Networks in the Presence of Noisy Labels Tail Annealing for Heavy-Tailed Flow Matching Variance-Reduced Manifold Sampling via Polynomial-Maximization Density Estimation Latent Laplace Diffusion for Irregular Multivariate Time Series Precision Physical Activity Prescription via Reinforcement Learning for Functional Actions Reducing Diffusion Model Memorization with Higher Order Langevin Dynamics Provably Data-driven Lagrangian Relaxation for Mixed Integer Linear Programming Can Adaptive Gradient Methods Converge under Heavy-Tailed Noise? 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On Variance Reduction in Learning Mean Flows
Juanwu Lu, Ziran Wang · 2026-05-10 · via stat updates on arXiv.org

One-step generative modeling has emerged as a leading approach to amortize the inference cost of diffusion and flow-matching models. Among distillation-free methods, MeanFlow training is notoriously unstable, with non-decreasing loss and unbounded gradient variance. In this work, we establish a theory that attributes this pathology to a misuse of the conditional velocity field: it plays two distinct statistical roles in the loss, both as an unbiased regression target and as a Monte Carlo control variate inside a Jacobi-vector product, with the original loss assigning the wrong coefficient to the latter. We derive the optimal coefficient in closed form, and show that a family of fixes in concurrent works corresponds to different practical realizations of the same optimum. A controlled sweep of this coefficient on two-dimensional benchmarks and on a latent Diffusion Transformer recovers the predicted bias-variance ordering. The optimal coefficient yields up to a %54 improvement in sample quality on two-dimensional benchmarks and a monotone FID trend at every matched-step DiT checkpoint. Crucially, the same DiT measurement also reveals a quantitative FID-MSE landscape mismatch: although gradient variance is minimized at an interior coefficient value, the coefficient that minimizes FID prefers the direct use of conditional velocity.