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We study the nonlinear $$\sigma$$-model in $${(d+1)}$$-dimensional spacetime with connected target space $$K$$ and show that, at energy scales below singular field comfigurations (such as vortices), it has an emergent non-invertible higher symmetry. The symmetry defects of the emergent symmetry are described by the $$d$$-representations of a discrete $$d$$-group $$\mathbb{G}^{(d)}$$ (i.e. the emergent symmetry is the dual of the invertible $$d$$-group $$\mathbb{G}^{(d)}$$ symmetry). The $$d$$-group $$\mathbb{G}^{(d)}$$ is determined such that its classifying space $$B\mathbb{G}^{(d)}$$ is given by the $$d$$-th Postnikov stage of $$K$$. In $(2+1)$D and for finite $$\mathbb{G}^{(2)}$$, this symmetry is always holo-equivalent to an invertible $${0}$$-form---ordinary---symmetry with potential 't Hooft anomaly. The singularity-free disordered phase of the nonlinear $$\sigma$$-model spontaneously breaks this symmetry, and when $$\mathbb{G}^{(d)}$$ is finite, it is described by the deconfined phase of $$\mathbb{G}^{(d)}$$ higher gauge theory. We consider examples of such disordered phases. We focus on a singularity-free $S^2$ nonlinear $$\sigma$$-model in $${(3+1)}$$D and show that it has an emergent non-invertible higher symmetry. As a result, its disordered phase is described by axion electrodynamics and has two gapless modes corresponding to a photon and a massless axion. Notably, this non-perturbative result is different from the results obtained using the $S^N$ and $$\mathbb{C}P^{N-1}$$ nonlinear $$\si$$-models in the large-$$N$$ limit.