Distribution Matching Distillation (DMD) distills multi-step diffusion models into few-step generators by minimizing reverse KL divergence. Despite its strong performance, DMD guides samples by local density alone, which introduces two limitations: teacher scores can be unreliable in regions of low teacher density, and the mode-seeking behavior of reverse KL can collapse the student onto a subset of the teacher modes. We first connect DMD to Wasserstein gradient flow, showing that its gradient follows from a fixed-point formulation with integral KL (IKL) as the energy functional. This perspective motivates augmenting IKL with an optimal transport term that addresses these limitations by guiding outlier samples toward the target and promoting mode coverage. We realize this term using Sinkhorn divergence estimated from finite batches. In practice, however, errors in the estimated Sinkhorn velocity can perturb in-domain samples for which IKL guidance is already accurate. To this end, we introduce sDMD, which adaptively activates the Sinkhorn correction based on discriminator outputs, focusing on outlier samples where IKL may be unreliable. With 2--4 sampling steps on FLUX.1-dev, Qwen-Image-20B, and Wan2.1-14B, sDMD outperforms distillation baselines on GenEval, DPG, WISE, and VBench while improving sample diversity over DMD2.

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