One-step generation stops drifting on minibatch proportions: swapping hard marginal constraints for soft penalties cuts CIFAR-10 FID from 8.10 to 4.51

The training objective for one-step generators no longer has to match minibatch marginals exactly; transported mass can adapt to sampling fluctuations. W-Flow previously used the balanced Sinkhorn divergence, whose coupling must exactly reproduce both input marginals, so when sampled proportions of different modes disagree, transport is forced between geometrically unrelated regions. On fixed-support and continuous two-mode distributions, the unbalanced minibatch-to-population velocity error is smaller as batch size, mode separation, and marginal relaxation vary; on CIFAR-10 at transport support 2, FID drops from 8.10 to 4.51.

The new method weights each displacement by transported mass while retaining W-Flow's cross-minus-self structure. In balanced transport the coupling marginals must equal the empirical marginals, so the source-averaged velocity is fixed by the empirical sample means and sampling fluctuations enter the velocity error directly. On MNIST, CIFAR-10, and ImageNet-100 the generator architecture, optimization protocol, and training budget are held fixed while only the transport objective changes; unconditional ImageNet-100 FID drops from 55.25 to 46.17.

The stability comparison measures each minibatch field against its own population field, not the population velocities of unbalanced versus balanced transport, and it does not guarantee better generation for arbitrary distributions. Controlled experiments cover a fixed-support two-particle model and a continuous two-Gaussian mixture; image experiments cover MNIST, CIFAR-10, and ImageNet-100 under matched training budgets.

The stability comparison does not compare the population velocities of unbalanced and balanced transport and does not guarantee better generation for arbitrary distributions; no method is provided for selecting the marginal penalty coefficient for a given setting. In the image results the class-conditional gain is smaller than the unconditional gain, consistent with class-wise transport reducing opportunities for between-class mismatch, although these results do not directly measure coupling mismatch.