Distribution Matching Distillation (DMD) provides an effective distribution-level correction for few-step generation, while relying on an auxiliary fake-score network to track the evolving generative distribution. Recent work combines DMD with a flow-map objective to exploit the benefits of both methods: mode-seeking and mode-covering behaviors. Since this fake-score network increases memory and update overhead, we study whether this explicit tracker can be avoided when the generator has a flow-map structure. In this work, we propose Fake-Score-network-Free DMD (FSF-DMD), a DMD-style correction for flow-map generators, replacing the auxiliary fake-score estimator with a generator-induced surrogate. We observe that this surrogate can be derived from the definition of the fake velocity under a certain perturbation assumption. Building on this insight, we derive a DMD-style objective without a fake-side network, extend it to backward simulation for flow maps, and to a self-teacher variant for training from scratch. In our ImageNet-1K $256\times 256$ experiments, FSF-DMD is competitive with the studied DMD baselines when initialized from pretrained networks and when trained from scratch.

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