We show that stochastically driven nonequilibrium conserved growth models admit generic strong coupling phases for sufficiently strong nonlocal chemical potentials underlying the dynamics. The models exhibit generic roughening transitions between perturbatively accessible weak coupling phases satisfying an exact relation between the scaling exponents in all dimensions $d$, and strong coupling phases. In dimensions at or below the critical dimension $d_c$, the latter phases are unstable and argued to be crumpled, and thus distinct from the well-known strong coupling rough phase of the Kardar-Parisi-Zhang equation in dimensions $d\ge 2$. At $d_c$, conventional spatiotemporal scaling in the weak coupling phase is logarithmically modulated and are exactly obtained.

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• Scaling laws of complex systems
• Nonequilibrium systems
• Kardar–Parisi–Zhang equation
• Mode coupling theory
• Renormalization group