The leading one-particle distributions for the inclusive reaction $\mathrm{pp}\to \mathrm{cX}$ ($c=p, {\pi }^{+}$) calculated in the diffractive-excitation model (DEM) are compared with the new CERN Intersecting Storage Rings data. For the pion distribution we show that a single Gaussian decay distribution, $\exp (-\lambda k^2)$, even with the added assumptions of momentum conservation and off-axis scattering of the clusters, is unable to fit the data. We then show that a pion decay distribution given by a sum of two Gaussians does fit both the fixed-$x$ and fixed-${P_{\perp }}^2$ distributions. The proton distributions are well fitted by a single Gaussian decay distribution. The proton spectrum exhibits a broad dip at $x\approx 0.85$ which is naturally explained in the DEM as protons emanating from a cluster ($x\lesssim 0.8$) and unexcited protons recoiling against a massive cluster ($x\gtrsim 0.9$).

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