The exact spectral density under these disorders is presented in Fig. in Supplementary Note 5. Fig. shows the cavity frequency dependence of k/k 0 for N = 10 3 at a collective Rabi splitting of Ω R = 100 cm -1 . The values of C j are taken from a normal distribution with standard deviation σ = ε • 0.1 cm -1 where the value of ε will determine the amount of variation in C j . For all cases considered here, we ensure that Λ is kept constant. Further, there is no angle disorder for the light-matter couplings, such that χ = 1 (c.f. Eq. 11). As one can see, increasing the disorder in the coupling (increasing ε) decreases the cavity effects. This is because adding disorder to the couplings allows the dark states coupling to R 0 to show up in J eff (ω) (see Supplementary Note 5, Fig. ), thus reducing the cavity effect as these dark modes have the same frequency as the vibrations outside the cavity. Nevertheless, the cavity modification effect will survive with a moderate magnitude of disorder, and the fundamental scaling indicated in Eq. 18 is also preserved (see Fig. in Supplementary Note 5). Fig. shows k/k 0 for N = 1000 at resonance for several values of ε and Ω R = 100 cm -1 , with both C j disorder (satisfies a normal distribution with σ = ε • 0.1 cm -1 ) and the random distribution of the angle between the dipole and cavity field {φ j } ∈ [0, φ], with φ changes from 0 (fully ordered) to π (isotropic). One can see that with a small C j disorder, the collective VSC effect will survive even for a random disorder of dipole angle for {φ j } ∈ [0, 3π/4], due to the fact that the dark modes have a small contribution in the spectral density (see Fig. of Supplementary Note 5). In the previous literature, the conceptual difficulties of explaining the VSC effects are largely due to the densely packed dark states that have the same energy as the original vibrational excitation , which will influence the rate constant in the same way outside the cavity. Here, we demonstrate that the extent of the dark states highly depends on the disorder of the system, where the cavity is able to modify the reaction rates even in the presence of such states.