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We study an idealized deterministic, continuous-time, vanishing-momentum version of this idea in the mean-field regime, where wide models are represented by probability measures on parameter space. Starting from normalized matrix flows, we introduce Spectral Wasserstein distances indexed by norms $\\gamma$ on positive semidefinite matrices: the trace norm gives classical $W_2$, the operator norm gives the Muon geometry, and Schatten norms interpolate between them. We develop the static Kantorovich formulation, a max-min robust-cost representation, Gaussian reductions extending the Bures formula, and for monotone norms, prove equivalence with a Benamou--Brenier formulation. 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We develop the static Kantorovich formulation, a max-min robust-cost representation, Gaussian reductions extending the Bures formula, and for monotone norms, prove equivalence with a Benamou--Brenier formulation. 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