DifferenceFlow: Dynamic Implicit Differences for One-Step Generative Modeling

MeanFlow has emerged as a powerful framework for training one-step generative models from scratch, without relying on pretrained teachers or multi-stage distillation. However, its derivative-based training target, which involves temporal derivatives evaluated through Jacobian-vector products, can be difficult to optimize early in training. Recent approaches such as AlphaFlow alleviate this difficulty through target interpolation, but their interpolation weight is heuristic rather than derived from the MeanFlow identity, which biases the target toward the instantaneous velocity. To address these limitations, we propose **DifferenceFlow**, a discrete formulation of MeanFlow that replaces the temporal derivative with a finite difference between model predictions along the same trajectory. Derived directly from the discretized MeanFlow identity, the DifferenceFlow target removes this bias and is second-order accurate in the interval length, while shrinking the interval during training yields a coarse-to-fine curriculum toward the original MeanFlow objective. On class-conditional ImageNet-1000 at $256\times 256$ resolution, our best model with fine-tuning outperforms state-of-the-art MeanFlow-based methods, achieving an FID of 2.29 with a single function evaluation.